Ram Murty - Publications by Year

The dvi files below are given for the benefit of those who may not have access to the respective journal. They may not contain changes made in the final proofs.
    1977
  1. Irrational numbers arising from certain differential equations, (with V. Kumar Murty), Canadian Math. Bulletin, 20 (1977) 117-120.

    1979

  2. Some results in number theory I, (with V. Kumar Murty), Acta Arithmetica, 35 (1979) 367-371.

    1980

  3. On the Redei zeta function, (with J.P. Kung and G.-C. Rota), Journal of Number Theory,12 (1980) 421-436.

    1982

  4. An Omega theorem for Ramanujan's tau function, (with R. Balasubramanian), Inventiones Mathematicae, 68 (1982) 241-252.
  5. Some Omega results for Ramanujan's tau function, Proceedings of the Number Theory Conference at Mysore, Springer Lecture Notes, 938 (1982) 123-137.
  6. Problems in enumeration of finite groups,, Proceedings of the Number Theory Conference at Mysore, Springer Lecture Notes, 938 (1982) 172-176.

    1983

  7. On the density of various classes of groups, (with V. Kumar Murty), Journal of Number Theory, 17 (1983) 29-36.
  8. On Artin's conjecture, Journal of Number Theory, 16 (1983) 147-168.
  9. Oscillations of Fourier coefficients of modular forms, Math. Annalen, 262 (1983) 431-446.

    1984

  10. An analogue of Artin's conjecture for abelian extensions, Journal of Number Theory, 18 (1984) 241-248.
  11. A remark on Artin's conjecture, (with R. Gupta), Inventiones Mathematicae, 78 (1984) 127-130.
  12. Prime divisors of Fourier coefficients of modular forms, (with V. Kumar Murty), Duke Math. Journal, 51 (1984) 57-77.
  13. On groups of squarefree order, (with V. Kumar Murty), Math. Annalen, 267 (1984) 299-309.
  14. On the number of groups of a given order, (with V. Kumar Murty), Journal of Number Theory, 18 (1984) 178-191.
  15. An analogue of the Erdös-Kac theorem for Fourier coefficients of modular forms, (with V. Kumar Murty), Indian Journal of Pure and Applied Mathematics, 15 (1984) 1090-1101.

    1985

  16. On the estimation of eigenvalues of Hecke operators, Rocky Mountain Journal of Mathematics, 15 (2) (1985) 521-533.

    1986

  17. Primitive points on elliptic curves, (with R. Gupta), Compositio Math., 58 (1986) 13-44.

    1987

  18. On the enumeration of finite groups, (with P. Erdös and V. Kumar Murty), Journal of Number Theory 25 (1987) 360-378.
  19. Some remarks on Artin's conjecture, (with S. Srinivasan), Canadian Math. Bulletin, 30 (1987) 80-85.
  20. Odd values of the Ramanujan tau function, (with V. Kumar Murty and T. N. Shorey), Bulletin Soc. Math. France, 115 (1987) 391-395.
  21. On the number of groups of squarefree order, (with S. Srinivasan), Canadian Math. Bulletin, 30 (4) (1987) 412-420.
  22. On the sieve of Eratosthenes, (with N. Saradha), Canadian Journal of Mathematics, 39 (5) (1987) 1107-1122.
  23. On the supersingular reduction of elliptic curves, Proceedings of the Indian Academy of Sciences, 97 (1-3) (1987) 247-250.
  24. A variant of the Bombieri-Vinogradov theorem, (with V. Kumar Murty), Number Theory, Proceedings of the 1985 Montreal conference, 7 (1987) 243-272.
  25. The Euclidean algorithm for S-integers, (with R. Gupta and V. Kumar Murty), Number Theory, Proceedings of the 1985 Montreal conference (ed. H. Kisilevsky and J. Labute), 7 (1987) 189-201.
  26. On Ramanujan's tau function, Ramanujan Revisited, Proceedings of the Illinois conference on Ramanujan, (1987) 269-288.
  27. An introduction to Selberg's trace formula, Journal of Indian Math. Society, 52 (1987) 91-126.

    1988

  28. Modular forms and the Chebotarev density theorem, (with V. Kumar Murty and N. Saradha), American Journal of Mathematics, 110 (1988) 253-281
  29. Primes in certain arithmetic progressions, Journal of the Madras University, (1988) 161-169.
  30. Recent developments in elliptic curves, Proceedings of the Ramanujan Centennial International Conference, 1 (1988) 45-53.
  31. Prime numbers, explicit formulas and the Riemann hypothesis, Quebec Math. Gazette, 12 (3) (1988) 3-15.
  32. Artin's conjecture for primitive roots, Math. Intelligencer, 10 (4) (1988) 59-67.

    1989

  33. Elliptic pseudoprimes, (with I. Miyamoto), Mathematics of Computation, 53 (187) (1989) 415-430.
  34. Elliptic pseudoprimes, II, (with R. Balasubramanian), Seminaire de Theorie des Nombres, Paris 1988-89, (1989) 13-25, Birkhauser-Verlag.
  35. L-series of automorphic forms on GL_3(R), (with Jeff Hoffstein), Number Theory, (J.-M. de Koninck and C. Levesque, eds.) (1989) 398-408, Walter de Gruyter.
  36. Review of An introduction to the theory of the Riemann zeta function, by S.J. Patterson, Cambridge Studies in Advanced Mathematics, Volume 14, Cambridge University Press, Cambridge and New York, (1988) 156 pages and of Introduction to analytic number theory, by A. G. Postnikov, Translations of Mathematical Monographs, Volume 68, American Mathematical Society, Providence, R.I., (1988) 320 pages in Bulletin of the American Mathematical Society, 20 (1989) 226-229.

    1990

  37. Cyclicity and generation of points mod p on elliptic curves, (with Rajiv Gupta), Inventiones Math., 101 (1990) 225-235.
  38. On simple zeroes of certain L-series, Number Theory (R. Mollin, ed.), (1990) 427-439, (Walter de Gruyter).
  39. Automorphic forms and analytic number theory (Editor), CRM, 1990.

    1991

  40. Mean values of derivatives of modular L-series, (with V. Kumar Murty), Annals of Mathematics, 133 (1991) 447-475.
  41. Elliptic curves and modular forms, Canadian Math. Bulletin, 34 (3) (1991) 375-384.

    1992

  42. Le programme de Langlands, Quebec Math. Gazette, 14 (2) (1992) 20-26.
  43. Theta functions, CRM, 1992.

    1993

  44. Base change and the Birch-Swinnerton-Dyer conjecture, Contemporary Mathematics, 143 (1993) 481-494, American Mathematical Society.
  45. An asymptotic formula by a method of Selberg, (with N. Saradha), Comptes Rendus Acad. Sci. (Canada), 15 (6) (1993) 273-277.
  46. Appendix to a paper of R.A. Smith, C.R.Math. Rep. Acad. Sci. Canada 15(1993) p. 91-98.
  47. A motivated introduction to the Langlands program, in Advances in Number Theory, (eds. F. Gouvêa and N. Yui), (1993) 37-66, Clarendon Press, Oxford.
  48. Theta functions: from the classical to the modern, CRM Proceedings and Lecture Notes, I, (editor).
  49. Topics in Number Theory, MRI Lecture Notes, 1993.

    1994

  50. On Zagier's cusp form and the Ramanujan tau function, (with Ashwaq Hashim), Proceedings of the Indian Academy of Sciences, 104 (1) (1994) 93-98.
  51. Selberg conjectures and Artin L-functions, Bulletin of the American Mathematical Society, 31 (1) (1994) 1-14.
  52. Finitely generated groups (mod p), Proceedings of the American Mathematical Society, 122 (1) (1994) 37-45.
  53. Strong multiplicity one for Selberg's class, (with V. Kumar Murty), Comptes Rendus Acad. Sci. Paris, 319 Series I (1994) 315-320.
  54. The Phragmen-Lindelof theorem and modular elliptic curves, (with Liem Mai), H. Rademacher Centenary Volume, Contemporary Math., 166 (1994) 335-340, Amer. Math. Society, Providence.
  55. A note on the quadratic twists of an elliptic curve, (with Liem Mai), Proceedings of the Ste. Adele Conference, (eds. H. Kisilevsky and R. Murty), CRM (1994) 121-124, American Math. Society, Providence.
  56. Elliptic curves and related objects, (Co-editor with H. Kisilevsky), CRM Proceedings and Lecture Notes, 4, 1994.

    1995

  57. The Euclidean algorithm in Galois extensions of Q, (with David Clark), Journal fur die reine und angewandte Mathematik, 459 (1995) 151-162.
  58. Supersingular primes common to two elliptic curves, (with E. Fouvry), London Mathematical Society Lecture Notes Series 215, Number Theory, Paris 1992-93, (ed. Sinnou David), (1995) 91-102, Cambridge University Press.
  59. Selberg's conjectures and Artin L-functions, II, in Current Trends in Mathematics and Physics, A tribute to Harish-Chandra, edited by S. D. Adhikari, Narosa Publishing House, 1995.
  60. On the rank of J0(N)(Q), in the Halifax Proceedings in Number Theory (ed. K. Dilcher), Canadian Mathematical Society 15 (1995) 263-277.
  61. Reflections on Fermat's Last Theorem, Elemente der Mathematik 50 (1995) 3-11.

    1996

  62. On the distribution of supersingular primes, (with Étienne Fouvry), Canadian Journal of Math. 48 (1) (1996) 81-104.
  63. A variation on a theme of Romanoff, (with M. Rosen and J. Silverman), International Journal of Mathematics, Vol. 7, No. 3 (1996) 373-391.
  64. Counting finite groups, in Analysis, Geometry and Probability, edited by Rajendra Bhatia, Hindustan Book Agency, (1996) 161-172.
  65. Stronger multiplicity one theorems for forms of general type on GL(2), (with C.S. Rajan), in Analytic Number Theory, Proceedings of the Number Theory Conference in honour of H. Halberstam, (eds. B. Berndt, H. Diamond, and A. Hildebrand), Progress in Mathematics, Vol. 139, (1996), 669-683, Birkhauser.
  66. Artin's conjecture and elliptic analogues, in Sieve Methods, Exponential Sums, and their Applications in Number Theory, (eds. G.R.H. Greaves, G. Harman, and M.N. Huxley) (1996) 325-344, Cambridge University Press.

    1997

  67. Congruences between modular forms, in Analytic Number Theory, (ed. Y. Motohashi), London Mathematical Society Lecture Notes 247 (1997) 313-320, Cambridge University Press.
  68. The ABC Conjecture and Exponents of Class Groups of Quadratic Fields, in Number Theory (edited by V. Kumar Murty and Michel Waldschmidt), Contemporary Math. 210, AMS, 1997, p. 85-95.
  69. Stronger multiplicity one for Selberg's Class, in Harmonic Analysis and Number Theory (Papers in honour of Carl Herz) (eds. S. Drury and R. Murty), Canadian Math. Society Conf. Proceedings, (1997) Vol. 21, pp. 133-142.
  70. Non-vanishing of L-functions, in Advances in Mathematical Sciences: CRM's 25 Years, (edited by Luc Vinet), CRM Proceedings and Lecture Notes, Volume 11, 1997, p. 319-328.
  71. Non-vanishing of L-functions and applications, (with V. Kumar Murty), Progress in Mathematics, 157, (Ferran Sunyer i Balauger Award Winning Monograph), Birkhauser, 1997.
  72. Harmonic analysis and number theory, (co-editor with S. Drury), CMS Conference Proceedings, Vol. 21, Amer. Math. Soc. 1997.

    1998

  73. Artin's conjecture for polynomials over finite fields, (with Erik Jensen), in Number Theory (edited by R.P. Bambah, V. Dumir and R.J. Hans Gill), Birkhauser-Verlag, 2000, pp. 167-181.
  74. Wieferich primes and Hall's conjecture, (with Satya Mohit), Comptes Rendus de l'Acad. Science (Canada), Vol. 20, No. 1, (1998) 29-32.
  75. Bounds for congruence primes, in Automorphic Forms, Automorphic Representations and Arithmetic, edited by R. Doran, Ze-Li Dou and G. Gilbert, Proceedings of Symposia in Pure Mathematics, Vol. 66, Part 1, pp. 177-192, Amer. Math. Soc., 1999.
  76. Problems in Algebraic Number Theory, (with Jody Esmonde), Graduate Texts in Mathematics, 190, Springer-Verlag, 1998.

    1999

  77. Exponents of class groups of quadratic fields, in Topics in Number Theory, (edited by S. Ahlgren, G. Andrews and K. Ono), pp. 229-239, 1999, Kluwer, Netherlands.
  78. On the order of a mod p, (with P. Erdös), CRM Proceedings and Lecture Notes, Volume 19, (1999) pp. 87-97.
  79. The Turan sieve method and some of its applications, (with Yu-ru Liu), Journal of the Ramanujan Mathematical Society, Vol. 13, No. 2, (1999) pp. 35-49.
  80. The pair correlation of zeros of functions in the Selberg class, (with A. Perelli), International Math. Res. Notices. (1999) Vol. 10, p. 531-545.
  81. The work of Sarvadaman Chowla, with V. Kumar Murty and K.S. Williams), in Volume 1, Collected Papers of Sarvadaman Chowla, pp. vii-xxviii, CRM, 1999.

    2000

  82. The work of Sarvadaman Chowla (with V. Kumar Murty and K.S. Williams), in the Collected Papers of Sarvadaman Chowla, CRM, 2000.
  83. Variations on a conjecture of Dedekind (with A. Raghuram), Journal of the Ramanujan Math. Society, 15, No. 2, (2000) pp. 75-95.
  84. Review of `Elementary Methods in Number Theory,' Bulletin of the Amer. Math. Soc., 2000, Vol. 38, Number 1, pp. 117-121.
  85. A simple derivation of $\zeta(1-k)=-B_k/k$, (with Marilyn Reece), Functiones et Approximatio, XXVIII (2000) 141-154.

    2001

  86. Some Remarks on the Riemann Hypothesis, in ``Cohomology of Arithmetic Groups, L-Functions and Automorphic Forms, (edited by T. N. Venkataramana), TIFR, Narosa Publishing House, pp. 180-196, Mumbai, India.
  87. Problems in Analytic Number Theory, GTM/RIM Vol. 206, Springer-Verlag, 2001.
  88. On Kummer's conjecture, (with Yiannis Petridis),Journal of Number Theory, Vol. 90, 2001, pp. 294-303.
  89. An Introduction to Artin L-functions, Journal of the Ramanujan Mathematical Society, Vol. 16, No. 3, 2001, pp. 261-307.
  90. Artin L-functions, in Class Field Theory - its centenary and prospect, (Tokyo, 1998), pp. 13-29, Advanced Studies in Pure Math., Vol. 30, Math. Soc. Japan, Tokyo, 2001.
  91. Exponents of class groups of quadratic function fields over finite fields, (with David Cardon), Canadian Math. Bulletin., Vol. 44 (4), 2001, pp. 398-407.
  92. Quadratic reciprocity via linear algebra, Bona Mathematica, Vol. 12, No. 4, (2001), 75-80.

    2002

  93. On the distinctness of decimations of l-sequences, (with M. Goresky, A. Klapper) in T. Helleseth, ed. Sequences and their applications, Proceedings of SETA '01, Discrete Mathematics and Computer Science, Springer-Verlag, New York, 2002.
  94. Explicit formulas for the pair correlation of zeros of functions in the Selberg class (with A. Zaharescu), Forum Math., Vol. 14, 2002, no. 1, 65-83.
  95. Averages of Exponential Twists of the Liouville function (with A. Sankaranarayanan), Forum Math., Vol. 14, 2002, no. 2, 273-291.
  96. Prime Numbers and Irreducible Polynomials, Amer. Math. Monthly, Vol. 109 (2002), no. 5, 452-458.
  97. Introduction to $p$-adic analytic number theory, AMS/IP Studies in Advanced Mathematics, 27, American Math. Society, Providence, RI, International Press, 2002, 149pp.
  98. Recent developments in the Langlands program, C. R. Math. Acad. Sci. Soc. R. Can. 24 (2002), no. 2, 33-54.
  99. Sieving using Dirichlet series,in Current Trends in Number Theory, edited by S. Adhikari, S.A. Katre, and B. Ramakrishnan, Hindustan Book Agency, 2002, pp. 111-124.
  100. The ABC conjecture and prime divisors of the Lucas and Lehmer sequences, (with Siman Wong), in Number Theory for the Millenium, Vol. 3, (edited by M. Bennett et al), 2002, pp. 43-54, A.K. Peters.

    2003

  101. On the uniform distribution of certain sequences, (with K. Srinivas), The Ramanujan Journal, 7 (2003), 185-192.
  102. On the number of real quadratic fields with class number divisible by 3,(with K. Chakraborty) Proceedings of the Amer. Math. Soc., 131(2003), no. 1, 41-44.
  103. Irreducibility of Hecke polynomials, (with Srinath Baba), Math. Research Letters, 10(2003), no. 5-6, 709-715.
  104. Ramanujan Graphs, Journal of the Ramanujan Math. Society, 18, No. 1, (2003), 1-20.
  105. Sieve methods, Siegel zeros and Sarvadaman Chowla, in Connected at Infinity, Texts and Readings in Mathematics, Hindustan Book Agency, 2003, pp. 18-35.

    2004

  106. Non-abelian generalizations of the Erdos-Kac theorem, (with F. Saidak), Canadian Journal of Math., Vol. 56 (2004), no. 2, 356-372.
  107. On decimations of l-sequences, (with M. Goresky, A. Klapper, and I. Shparlinski), SIAM J. Discrete Math., Vol. 18 (2004), no. 1, p. 130-140.
  108. Euclidean rings of Algebraic Integers, (with M. Harper) Canadian Journal of Math., Vo.. 56 (2004), no. 1, p. 71-76.
  109. On the p-adic series $\sum_{n=1}^\infty n^k n! $ (with S. Sumner), CRM Lecture Notes 36, pp. 219-227, Amer. Math. Society, Providence, RI 2004.
  110. Lectures on Automorphic L-functions, (with James Cogdell and Henry Kim), Fields Institute Monograph Series, Volume 20, 2004, 283p.
  111. Pair Correlation Conjecture and the Chebotarev Density Theorem (with V. Kumar Murty), preprint.
  112. Summatory functions of elements in the Selberg class, (with Wentang Kuo), Algebraic Groups and arithmetic, Tata Institute of Fundamental Research, 2004, pp. 525-538.
  113. An application of Mumford's gap principle, (with Jung-Jo Lee), Journal of Number Theory, 105 (2004), no. 2, 333-343.
  114. Cyclicity of elliptic curves modulo p and elliptic curve analogues of Linnik's problem, (with A. Cojocaru), Math. Annalen, 330 (2004), no. 3, 601-625.

    2005

  115. Ramanujan graphs and zeta functions, in Algebra and Number Theory, (edited by R. Tandon), Hindustan Book Agency, 2005, pp. 269-280.
  116. On a conjecture of Birch and Swinnerton-Dyer, (with Wentang Kuo), Canadian Journal of Math., 57 (2005), no. 2, 328-337.
  117. Problems in Algebraic Number Theory (with J. Esmonde), Second Edition, Graduate Texts in Mathematics, 190, Springer-Verlag, 2005.
  118. Sieve methods in combinatorics, (with Yu-Ru Liu), Journal of Combinatorial Theory, Series A., 111 (2005), no. 1, 1-23.
  119. Quadratic reciprocity via theta functions, (with Allison Pacelli), Ramanujan Math. Society Lecture Notes, Volume 1, (2005), pp. 107-116.
  120. The square sieve and the Lang-Trotter conjecture, (with A. Cojocaru and E. Fouvry), Canadian Journal of Math., 57 (2005), no. 6, 1155-1177.

    2006

  121. The weighted Turan sieve,(with Yu-Ru Liu), Journal of Number Theory, 116 (2006), no. 1, 1-20.
  122. Spectral Estimates for Abelian Cayley Graphs, (with J. Friedman and J.-P. Tillich), J. Combin. Theory Ser. B. 96 (2006), no. 1, 111-121.
  123. Multiple Hurwitz zeta functions, (with K. Sinha), in Multiple Dirichlet series, automorphic forms, and analytic number theory, Proc. Symp. Pure Math., 75 (2006), 135-156.
  124. Applications of Sieve Methods, (with A. Cojocaru), Cambridge University Press, London Mathematical Society Student Texts, 66 (2006), 224p.
  125. Irreducible polynomials over number fields, (with Jasbir Chahal), in The Riemann zeta function and related themes: papers in honour of Professor K. Ramachandra, Ramanujan Math. Soc. Lecture Notes Ser., 2 (2006), 39-43.
  126. Prime numbers in certain arithmetic progressions, (with N. Thain), Funct. Approx. Comm. Math., 35 (2006), 249-259.

    2007

  127. Pick's theorem via Minkowski's theorem, (with N. Thain), American Math. Monthly, 114 (2007), 732-736.
  128. Transcendental values of the digamma function, (with N. Saradha), Journal of Number Theory, 125 (2007), no. 2, 298-318.
  129. Dirichlet series and hyperelliptic curves, (with Jung-Jo Lee), Forum Math., 19 (2007), no. 4, 677-705.
  130. Sudoku squares and chromatic polynomials, (with A. Herzberg), Notices of the Amer. Math. Soc., 54 (2007) no. 6, 708-717.
  131. Counting integral ideals in a number field, (with J. Van Order), Expo. Math., 25 (2007), no. 1, 53-66.
  132. Odd values of Fourier coefficients of certain modular forms, (with V. Kumar Murty), International Journal of Number Theory, 3 (2007), 455-470.
  133. Group structure of elliptic curves over finite fields and applications, in Topics in geometry, coding theory and cryptography, Algebr. Appl., 6, Springer, Dordrecht, 2007, 167-198.
  134. Representations of integers by certain positive definite binary quadratic forms, (with R. Osburn), Ramanujan Journal, 14 (2007) no. 3, 351-359.

    2008

  135. On a conjecture of Shorey, (with V. Kumar Murty), Diophantine equations, Tata Institute for Fundamental Research Studies, Volume 20, 2008, 167-176.
  136. Transcendental values of the p-adic digamma function (with N. Saradha), Acta Arithmetica, 133(2008), no. 4, , pp. 349-362.
  137. Uniform distribution of zeros of Dirichlet series, (with A. Akbary), CRM Conference Proceedings: Anatomy of Integers, Lecture Notes Ser., Volume 46, 2008, pp. 143-158.
  138. Summation methods and distribution of eigenvalues of Hecke operators, (with S. Gun and P. Rath), Funct. Approx. Comment. Math., 39 (2008), part 2, 191-204.
  139. On a generalisation of Artin's conjecture, (with C. Franc), Pure and Applied Math. Quarterly, 4 (2008), no. 4, 349-362.
  140. Transcendental numbers and zeta functions, Math. Student, 77 (2008), no. 1-4, 87-101.
  141. Polynomials assuming square values,, Number Theory and Discrete Geometry, Ramanujan Math. Society Lecture Notes Ser., 6, 155-163, 2008.
  142. Expander graphs and gaps between primes, (with S. Cioaba), Forum Math., 20 (2008), 745-756.

    2009

  143. Special values of the polygamma functions, (with N. Saradha), International Journal of Number Theory 5(2009), no. 3, 681-714.
  144. Effective equidistribution of eigenvalues of Hecke operators, (with K. Sinha), J. Number Theory, 129 (2009), no. 3, 681-714.
  145. Linear independence of the digamma function and a variant of a conjecture of Rohrlich, (with S. Gun and P. Rath), Journal of Number Theory, 129 (2009), no. 8, 1858-1873.
  146. Counting squarefree discriminants of trinomials under abc,(with A. Mukhopadhyay and K. Srinivas), Proc. Amer. Math. Soc., 137 (2009), no. 10, 3219-3226.
  147. Transcendence of the log gamma function and some discrete periods, (with S. Gun and P. Rath), Journal of Number Theory, 129 (2009), no. 9, 2154-2165.
  148. The generalized Artin conjecture and arithmetic orbifolds, (with K. Petersen), CRM Conference Proceedings, Volume 47 (2009), 259-265.
  149. A first course in graph theory and combinatorics, (with S. Cioaba), Hindustan Book Agency, 55, 2009, New Delhi. Errata
  150. The Sato-Tate conjecture and generalizations, (with V. Kumar Murty), in Current Trends in Science, Platinum Jubilee Special, edited by N. Mukunda, 2009, 639-646.
  151. Variations of Sato-Tate Conjecture, Number Theory and applications, Hindustan Book Agency, New Delhi, 2009, 127-138.

    2010

  152. Small solutions of polynomial congruences, Indian J. Pure Appl. Math., 41 (2010), no. 1, 15-23.
  153. Factoring newparts of Jacobians of certain modular curves, (with K. Sinha), Proceedings of the Amer. Math. Society, 138 (2010), no. 10, 3481-3494.
  154. Euler-Lehmer constants and a conjecture of Erdos (with N. Saradha), Journal of Number Theory, 130(2010), no. 12, 2671-2682.
  155. A combinatorial identity for studying Sato-Tate problems, (with S.J. Miller and F. Strauch), Rend. Sem. Mat. Univ. Politc. Torino, 68 (2010), No. 4, 337-348.
  156. Some recent developments in number theory. Math. Newsl. 19 (2010), Sp. Number 1, 175-182.

    2011

  157. On a problem of Ruderman, (with V. Kumar Murty), American Math. Monthly, 118 (2011), 644-650.
  158. Zeros of Ramanujan polynomials (with C. Smyth and R.J. Wang), Journal of the Ramanujan Mathematical Society, 26, No. 1, (2011), 107-125.
  159. The class number of Q(\sqrt{-p}) and digits of 1/p (with R. Thangadurai), Proceedings of the American Mathematical Society, 139 (2011), no. 4, 1277-1289.
  160. Effective equidistribution and the Sato-Tate law for families of elliptic curves, (with Steven J. Miller), Journal of Number theory, 131 (2011)25-44.
  161. A problem of Chowla revisited, (with V. Kumar Murty), Journal of Number Theory, 131 (2011), 1723-1733.
  162. On a conjecture of Chowla and Milnor (with S. Gun and P. Rath), Canadian Journal of Mathematics, 63(2011), 1328-1344.
  163. Transcendental nature of special values of L-functions, (with S. Gun and P. Rath), Canadian Journal of Mathematics, 63(2011), 136-152.
  164. Transcendental values of certain Eichler integrals, (with S. Gun and P. Rath), Bulletin of the London Mathematical Society, 43 (2011), no. 5, 939-952.
  165. L-series and transcendental numbers, Lecture Notes of the Ramanujan Mathematical Society, 15 (2011), 89-101.
  166. Transcendental values of class group L-functions, (with Kumar Murty), Math. Annalen, 351 (2011), 835-855.
  167. Some remarks on a problem of Chowla,, Annales des sciences mathematiques de Quebec, 35 (2011), 229-237.
  168. On the transcendence of certain infinite series, , (with C. Weatherby), International Journal of Number Theory, Vol. 7, Number 2, (2011), 323-339.
  169. Algebraic Independence of Values of Modular Forms,, (with S. Gun and P. Rath), International Journal of Number Theory, Volume 7, Number 4, (2011), 1065-1074.

    2012

  170. A variant of the Lang-Trotter conjecture,, (with V. Kumar Murty), in Number Theory, Analysis and Geometry, edited by D. Goldfeld et al., In Memory of Serge Lang, Springer, 2012, 461-474.
  171. The uncertainty principle and a generalization of a theorem of Tao, (with Junho Peter Whang), Linear Algebra and its applications, 2012 (doi: 10.1016/j.laa.2012.02.009)
  172. Grimm's conjecture and smooth numbers, (with S. Laishram), Michigan Math. Journal, 61 (2012), 151-160.
  173. Transcendental values of class group L-functions, II, (with Kumar Murty), Proceedings of the American Math. Society, January 30, 2012.
  174. A Problem of Fomenko's related to Artin's conjecture, (with A. Felix), International Journal of Number Theory, Vol. 8, No. 7, (2012), 1-37.
  175. A derivation of the Hardy-Ramanujan formula from an arithmetic formula, (with M. Dewar), Proceedings of the American Mathematical Society, 141 (2012), 1903-1911.
  176. Linear independence of Hurwitz zeta values and a theorem of Baker-Birch-Wirsing over number fields, (with S. Gun and P. Rath, Acta Arithmetica, 155 (2012), no. 3, 297-309.
  177. On a paper of S.S. Pillai, (with R. Thangadurai), Proc. Indian Acad. Sci. (Math. Sci.) 122 (2012), 1-13.

    2013

  178. Book review of ``A Passage to Infinity" by G.G. Joseph, Sage Publications, 2009, 220p. in Hardy-Ramanujan Journal, 36 (2013), 43-46.
  179. The Fibonacci zeta function, Automorphic representations and L-functions, TIFR Conference Proceedings, edited by D. Prasad, C.S. Rajan, A. Sankaranarayanan, J. Sengupta, Hindustan Book Agency, New Delhi, India, 2013.
  180. The abc conjecture and non-Wieferich primes in arithmetic progressions, (with H. Graves), Journal of Number Theory, 133 (2013), 1809-1813.
  181. An asymptotic formula for the coefficients of $j(z)$, (with M. Dewar), International Journal of Number Theory, 9 (2013), 1-12.
  182. The Euclidean algorithm for number fields and primitive roots, (with K. Petersen), Proceedings of the American Mathematical Society, 141 (2013), 181-190.
  183. A family of number fields with unit rank at least 4 that has Euclidean ideals, (with H. Graves), Proceedings of the American Math Society, 141 (2013), 2979-2990.
  184. A Bombieri-Vinogradov theorem for all number fields, (with K. Petersen), Transactions of the American Math. Society, 365 (2013), 4987-5032.
  185. Modular forms and effective Diophantine approximation, (with H. Pasten), Journal of Number Theory, 133 (2013), 3739-3754.
  186. Transcendence of generalized Euler constants, (with A. Zaytseva), American Math. Monthly, 120 (2013), no. 1, 48-54.
  187. Ramanujan's proof of Bertrand's postulate, (with J. Meher), American Math. Monthly, 120 (2013), 650-653.
  188. On the asymptotics for invariants of elliptic curves modulo $p$ (with A. Felix), J. Ramanujan Math. Society, 28., No. 3 (2013), 271-298.
  189. Ramanujan and the zeta function, Journal of the Indian Math. Society, Special volume to commemorate the 125th birth anniversary of S. Ramanujan, 2013.
  190. The partition function revisited, The Legacy of Srinivasa Ramanujan, Proceedings of the Conference marking the 125th anniversary of Srinivasa Ramanujan, New Delhi, India, 2012.
  191. Ramanujan series for arithmetical functions, Hardy-Ramanujan Journal, 36 (2013), 21-33.
  192. The twin prime problem and generalizations, Resonance, August 2013, 712-731.

    2014

  193. Special values of the gamma function at CM points, (with C. Weatherby), Ramanujan Journal, published online 14 January 2014.
  194. Non-vanishing of Dirichlet series with periodic coefficients,(with T. Chatterjee),Journal of Number Theory, 145 (2014), 1-21.
  195. Sign changes of Fourier coefficients of half-integral weight cusp forms,(with J. Meher), International Journal of Number Theory, 2014.
  196. Book review of "Indian Philosophy in English: From Renaissance to Independence" in Essays in Philosophy, Volume 15, (2014), 184-191.
  197. A note on special values of L-functions, (with S. Gun and P. Rath), Proceedings of the American Mathematical Society, 142, No. 4, (2014), 1147-1156.
  198. Divisors of Fourier coefficients of modular forms, (with Sanoli Gun), New York Journal of Mathematics, 20(2014), 1-11.
  199. Counting squarefree values of polynomials with error term, (with H. Pasten), International Journal of Number Theory, 2014.
  200. An elliptic analogue of a theorem of Hecke, (with A. Vatwani), Ramanujan Journal, October 2014.
  201. Ramanujan-Fourier series and a theorem of Ingham, (with H. Gadiyar and R. Padma), Indian Journal of Pure and Applied Math., 45 (2014), 691-706.
  202. Some remarks on iterated maps of natural numbers, (with A. Herzberg), Resonance, November, 2014, 1038-1046.
  203. New developments on the twin prime problem and generalizations, Hardy-Ramanujan Journal, 37 (2014), 13-19.

    2015

  204. A very simple proof of Stirling's formula, (with K. Sampath), Mathematics Student, 84 (2015), 129-133.
  205. On the parity of the Fourier coefficients of $j$-function, (with R. Thangadurai), Proceedings of the American Mathematical Society, 2015.
  206. On a conjecture of Erdos and certain Dirichlet series, (with T. Chatterjee), Pacific Journal of Mathematics, 275 (2015), 103-113.
  207. On the asymptotic formula for the Fourier coefficients of j-function, (with K. Sampath), Kyushu Journal of Mathematics, 2015.
  208. On the error term in a Parseval type formula in the theory of Ramanujan expansions,(with B. Saha), Journal of Number Theory, 2015.
  209. Transcendental values of the incomplete gamma function and related questions, , (with E. Saha), Archiv der Mathematik, 2015.
  210. Some remarks on automorphy and the Sato-Tate conjecture, (with V. Kumar Murty), in Advances in the Theory of Numbers, Proceedings of the 13th conference of CNTA, 2015, pp. 159-168.
  211. The Generalized Dedekind Determinant, (with Kaneenika Sinha), Contemporary Math., 655 (2015), 153-164.

    2016

  212. A generalization of Euler's theorem for ζ(2k),, (with C. Weatherby), American Mathematical Monthly, 123 (2016), 53-65.
  213. On the error term in a Parseval type formula in the theory of Ramanujan expansions II, (with G. Coppola and B. Saha), Journal of Number Theory, 160 (2016), 700-715.
  214. On the nature of eγ and non-vanishing of L-series at s=1/2, , (with N. Tanabe), Journal of Number Theory, 161 (2016), 444-456.
  215. A note on q-analogues of Dirichlet L-functions, (with A. Hamieh), International Journal of Number Theory, 12(2016), 765-773.
  216. Some remarks related to Maeda's conjecture,(with K. Srinivas), Proceeding of the American Math. Society, 2016.
  217. Some remarks on the discrete uncertainty principle, in Highly Composite: Papers in number theory, Ramanujan Mathematical Society Lecture Notes Series, No. 23, (2016), pp. 77-85.
  218. Generalization of an identity of Ramanujan, (with S. Gun), Journal of the Ramanujan Math. Society, 31 (2016), 125-135.
  219. Oscillations of coefficients of Dirichlet series attached to automorphic forms, (with J. Meher), Proceedings of the Amer. Math. Society, 2016.
  220. Generalization of a theorem of Hurwitz, (with J.J. Lee and D. Park), Journal of the Ramanujan Math. Society, 31 (2016), 215-226
  221. On sign changes for almost prime coefficients of half-integral weight modular forms, (with S. Krishnamoorthy), Mathematika 62 (2016), 801-810.
  222. Distinguishing Hecke eigenforms, (with Sudhir Pujahari), Proceedings of the American Math. Society, 2016.

    2017

  223. Fundamental units and consecutive squarefull numbers,(with K. Aktas), International Journal of Number Theory, 13(2017), no. 1, 243-252.
  224. Bertrand's postulate for number fields,, (with T. Hulse), Colloquium Mathematicum, 147 (2017), no. 2, 165-180.
  225. A higher rank Selberg sieve with an additive twist and applications, (with A. Vatwani), Fonctiones et Approximatio, 2017.
  226. Finite Ramanujan expansions and shifted convolution sums of arithmetical functions, (with G. Coppola and B. Saha), Journal of Number Theory, 174 (2017), 78-92.
  227. The analog of the Erdos distance problem in finite fields, (with S. D. Adhikari and A. Mukhopadhyay),International Journal of Number Theory, 2017.
  228. The art of research,, Mathematics Student, 86 (2017), 121-131.
  229. Evaluation of the quadratic Gauss sum,(with Siddhi Pathak), Mathematics Student, 86 (2017), 139-150.
  230. On the number of special numbers, (with K. Aktas), Proceedings of the Indian Academy of Sciences, 127 (2017), no. 3, 423-430.
  231. How I discovered Euclidean proofs,, Nieuw Archief, 5/18 (2017), no. 2, 101-102.
  232. Twin primes and parity problem, (with A. Vatwani), Journal of Number Theory, 180(2017), 643-659.
  233. Elliptic curves, L-functions and Hilbert's tenth problem, (with H. Pasten), Journal of Number Theory, 2017.
  234. On the transcendence of certain Petersson inner products, (with V. Kumar Murty), Bulletin of the Iranian Math. Society, 43 (2017), no. 4, 313-316 (dedicated to Freydoon Shahidi on his 70th birthday).

    2018

  235. Finite Ramanujan expansions and shifted convolution sums of arithmetical functions, II,(with G. Coppola), Journal of Number Theory 185(2018) 16-47
  236. A smooth Selberg sieve and applications, (with A. Vatwani), Geometry, algebra, number theory, and their information technology applications, 291-315, Springer Proc. Math. Stat., 251, Springer, Cham, 2018.
  237. Transcendental numbers and special values of Dirichlet series, Contemporary Math., Vol. 701 (2018).
  238. A vanishing criterion for Dirichlet series with periodic coefficients, (with T. Chatterjee and S. Pathak), Contemporary Math., Vol. 701 (2018).
  239. A remark on a conjecture of Chowla, (with A. Vatwani), J. Ramanujan Math. Society, 33, No. 2, (2018), 111-123.
  240. Special values of derivatives of L-series and generalized Stieltjes constants (with Siddhi Pathak), Acta Arithmetica 184 (2018), no. 2, 127-138.
  241. A remark on the Lang-Trotter and Artin conjectures, (with A. Vatwani), Proceedings of the American Math. Society, 2018.
  242. Admissible primes and Euclidean quadratic fields, (with K. Srinivas and M. Subramani), Journal of the Ramanujan Mathematical Society, 33 (2018), 135-147.
  243. Simultaneous non-vanishing and sign changes of Fourier coefficients of modular forms, (with Moni Kumari), International Journal of Number Theory, 14 (2018), no. 8, 2291-2301.
  244. Transcendental sums related to the zeros of zeta functions, (with S. Gun and P. Rath), Mathematika 64 (2018), 875-897.
  245. Overview of the Work of Kumar Murty (with A. Akbary and S. Gun), in Geometry, Algebra, Number Theory and Their Information Technology Applications, Springer Proceedings In Mathematics and Statistics, edited by A. Akbary and S. Gun, Volume 251, Springer, 2018, 1-18.
  246. A smooth Selberg sieve and applications, (with A. Vatwani), in Geometry, Algebra, Number Theory and Their Information Technology Applications, Springer Proceedings In Mathematics and Statistics, edited by A. Akbary and S. Gun, Volume 251, Springer, 2018, 291-315.
  247. The Chebotarev density theorem and the pair correlation conjecture, (with V. Kumar Murty and Peng-Jie Wong), Journal of the Ramanujan Mathematical Society, 33 (2018), no. 4, 399-426.
  248. Finite order elements in the integral symplectic group, (with K. Balasubramanian and K. Shankhadhar), Journal of the Ramanujan Math. Society, 33 (2018), no.4, 427-433.
  249. The zeta Mahler measure of (zn-1)/(z-1), (with A. Biswas), Hardy-Ramanujan Journal 41 (2018), 77-84.

    2019

  250. A lower bound for the two-variable Artin conjecture and prime divisors of recurrence sequences, (with F. Séguin and C.L. Stewart) Journal of Number Theory 194 (2019), 8-29.
  251. The error term in the Sato-Tate theorem of Birch, (with N. Prabhu), Bulletin of the Australian Math. Society, 2019.
  252. On a conjecture of Bateman about r5(n) (with A. Kar), Journal of the Ramanujan Math. Society, 34 (2019), no. 1, 133-142.
  253. A simple proof that ζ(2)= π2/6 Mathematics Student, 88 (2019), 113-115.
  254. Prime divisors of sparse values of cyclotomic polynomials and Wieferich primes, (with F. Seguin), Journal of Number Theory, 201 (2019) 1-22.
  255. Diophantine m-tuples with the property D(n), (with R. Becker), Glasnik Matematicki, 54 (2019), 65-75.
  256. The Cauchy-Schwarz inequality in mathematics, physics and statistics, Math. Student, Volume 88 (2019).
  257. Class numbers of quadratic fields, (with A. Bhand), Hardy-Ramanujan Journal, 42(2019), 1-9.

    2020

  258. The Paley graph conjecture and Diophantine m-tuples, (with A. Guloglu), Journal of Combinatorial Theory, Series A 170(2020), 105-155.
  259. Central limit theorems for sums of quadratic characters, Hecke eigenforms, and elliptic curves, (with N. Prabhu), Proceedings of the American Mathematical Society, 148 (2020), no.3, 965-977.
  260. Relations between certain power series and functions involving zeros of zeta functions, (with S. Pathak), Proceedings of Ropar Conference, RMS Lecture Notes Series, No. 26, 2020, pp. 203-222.
  261. Artin's primitive root conjecture for function fields revisited, (with Seoyoung Kim), Finite Fields and Their Applications, 67(2020)101713. Corrigendum.
  262. Convolution of values of the Lerch zeta function, (with Siddhi Pathak), Journal of Number Theory, 217 (2020), 1-22.
  263. The central limit theorem in algebra and number theory, (with Arpita Kar), in Modular Forms and Related Topics in Number Theory, Springer, 2020.
  264. A Second Course in Analysis, IMSC Lecture Notes Series, 2020.
  265. A localized Erdos-Kac theorem, (with Anup Dixit), Hardy-Ramanujan Journal,43 (2020).
  266. Ramanujan graphs: an introduction, Indian Journal of Discrete Math., Vol. 6, No. 2 (2020), 91-127.

    2021

  267. A note on values of the Dedekind zeta function at odd positive integers, (with S. Pathak), International Journal of Number Theory, 2021.
  268. A variant of the Hardy-Ramanujan theorem, (with V. Kumar Murty), Hardy-Ramanujan Journal, 44(2021), 32-40.
  269. On the normal number of prime factors of sums of Fourier coefficients of eigenforms, (with V. Kumar Murty and Sudhir Pujahari), Journal of Number Theory,(2021).
  270. Smooth arithmetical sums over k-free integers , (with Francesco Cellarosi), Journal of the Ramanujan Math. Society 36,No. 2(2021)147-156.

    2022

  271. Mathematics of the Pandemic, (with V. Kumar Murty), in Mathematics of Public Health, edited by V.K. Murty and J. Wu, Fields Institute Communications 85, 2022, pp. 323-353.
  272. Generalized Diophantine $m$-tuples, (with A. Dixit and S. Kim) Proceedings of the American Math. Society, 150 (2022), No. 4, 1455-1465.
  273. The Okada space and vanishing of L(1,f) (with S. Pathak), Fonctiones et Approximatio, 66 (2022), 35-57.
  274. On the density of irreducible polynomials which generate k-free polynomials over function fields (with Seoyoung Kim), Function Fields and Their Applications, 76 (2022), 101979.

    2023

  275. From the Birch and Swinnerton-Dyer conjecture to Nagao's conjecture, (with Seoyoung Kim), Mathematics of Computation, Volume 92, Number 339, (2023), 385-408.
  276. On Hasse's inequality, Expositiones Mathematicae, 2023.
  277. On Ihara's conjectures for EulerKronecker constants, (with A. Dixit), Acta Arithmetica, Schinzel Volume, 2023.
  278. Irrationality of zeros of the digamma function, in Number Theory in Memory of Eduard Wirsing, 2023.
  279. On the Hardy-Littlewood prime tuples conjecture and higher convolutions of Ramanujan sums, (with Sneha Chaubey and Shivani Goel), Fonctiones et Approximatio, 2023, 1-15.
  280. An all-purpose Erdos-Kac theorem, (with V. Kumar Murty and S. Pujahari) Math. Zeitschrift, (2023), 18p.

    2024

  281. The large sieve revisited, Acta Arithmetica, 2024.
  282. A simple proof of the Wiener-Ikehara Tauberian theorem, (with Akshaa Vatwani and Jagannath Sahoo), Expositiones Mathematicae, 42 (2024) 125570.
  283. A note on the two variable Artin's conjecture, (with Suhita Hazra and Jyothsnaa Sivaraman), Journal of Number Theory, 262 (2024), 161-185.
  284. Unimodal sequences: from Isaac Newton to June Huh, International Journal of Number Theory, 2024.
  285. A function related to the MordellWeil rank of elliptic curves, (with A. B. Dixit, S.S. Pathak), International Journal of Number Theory, 2024.