Ram Murty

A. V. Douglas Distinguished University Professor and Queen's Research Chair
E-mail:murty at mast dot queensu dot ca

Math/Stat Department Home Page
Rota's Ten Lessons

Office: Jeffery Hall, Room 517
Office Hours: By appointment
Office Phone: (613) 533-2413
Office FAX: (613) 533-2964
Department of Mathematics, Jeffery Hall,
99 University Avenue, Queen's University,
Kingston, Ontario, K7L 3N6, Canada

Courses for 2023-2024

Math 891: (Fall Semester)
Core Analysis I
Text:M. Ram Murty, A Second Course in Analysis
Mon., 3.30-4.30pm, Jeff 422
Wed., 2.30-3.30pm,   Jeff 422
Thu., 4.30-5.30pm,   Jeff 422
Phil 410/810: (Fall Semester)
Topics in the History of Philosophy: Indian Philosophy
Texts: M. Ram Murty, Indian Philosophy: An introduction, Broadview Press, 2012.
S. Radhakrishna and C. Moore, A sourcebook of Indian philosophy, Princeton University Press, 1967
Swami Vivekananda, Yogas and other works, edited by Swami Nikhilananda, Ramakrishna-Vivekananda Center, New York, 1957
Time: Thurs., 1130am-2.20pm,
Place:Jeffery Hall 102.

Math 381: (Winter Semester)
Mathematics with a Historical Perspective
Text:C.B. Boyer, A History of Mathematics, 3rd edition
Tue. 8.30-9.20am Jeff 126
Wed. 10.30-11.20am Jeff 126
Fri. 9.30-10.20am Jeff 126
Math 418/Mthe 418/Math 818(Winter Semester)
Number Theory and Cryptography
Text: N. Koblitz, A Course in Number Theory and Cryptography, 2nd Edition
Tues 12:30pm - 1:20pm Miller 201
Thurs 11:30am - 12:20pm Miller 201
Fri 1:30pm - 2:20pm Miller 201

Recent Books

            Introduction to the Circle Method
            A Second Course in Analysis
            Hilbert's Tenth Problem
            Panorama Lectures:
Ramanujan Conjectures and Zeta Functions
Problems in the
Theory of Modular Forms
    Transcendental Numbers
      Indian Philosophy:
      An Introduction    
The Mathematical Legacy
of Srinivasa Ramanujan
A First Course in Graph
Theory and Combinatorics
Automorphic L-functions
(with Kaneenika Sinha)
American Mathematical Society,
IMSC Lecture
Notes - 4
(with B. Fodden)
American Mathematical Society,
Ramanujan Mathematical Society,
(with M. Dewar & H. Graves),
IMSc Lecture Notes, 2015
(with P. Rath),
Springer, 2014.
Broadview Press, 2013. (with V. Kumar Murty),
Springer, 2012. errata
(with S. Cioaba),
HBA, 2009 errata
(with J. Cogdell and H. Kim),
Fields Inst./AMS, 2009.

Earlier Books

Problems in Analytic
Number Theory
Intro. to sieve methods
and their applications
Problems in Algebraic
Number Theory, 2nd Ed.
Introduction to p-adic
analytic number theory,
Non-vanishing of L-functions
and applications
Springer, 2nd edition, 2008 (with A. Cojocaru)
Cambridge Univ. Press,
(with J. Esmonde),
Springer 2005
International Press, 2002 (with V. Kumar Murty)
Balaguer Prize Book
Birkhauser, 1997

Useful Links

  • Mathscinet Search
  • Number Theory Web
  • Kumar Murty's Page
  • Library/Queen's University
  • JSTOR(Mathematics)
  • Some vintage photos

    Some of my Youtube lectures

  • Mathematics, Measurement and Information Technology, IMSC (July 6, 2015)
  • A short course on modular forms (10 lectures)(IISER, Bhopal, August 2016)
  • A mini-course on analytic number theory (8 lectures (IMSC. Chennai,July, 2016)
  • The Ramanujan tau function (Talk at IMSC, December, 2019)
  • Some remarks on the Birch-Swinnerton-Dyer conjecture (May 27, 2020)
  • Ramanujan Yatra (Talk on the tau function, Vigyan Prasar, September 24, 2020)
  • Ramanujan Graphs: a retrospective (Virtual talk at Kerala School of Mathematics, December 2020)
  • The Art and Science of Research (4 August 2021, Virtual Talk, IIT Delhi)
  • The arithmetic of function fields over finite fields, September 21, 2021.
  • The Art of Research (Virtual talk given at Chennai Math Institute, January 9, 2022)
  • The Divinity of Numbers (Virtual Interview of Tattva Deep, January 29, 2022)
  • Brain networks and graph theory Mathematical Teachers Association of India, September 10, 2022.
  • Fermat quotients and the Ankeny-Artin-Chowla conjecture,virtual talk at the Kerala School of Mathematics, November 22, 2022.
  • Probability and Number Theory (10 lectures) (Harish-Chandra Research Institute, Prayagraj, India, December 15-20, 2022)
  • Ramanujan and His Legacy (Talk at IMSC, December 26, 2022)
  • Unimodal sequences: from Isaac Newton to June Huh (Virtual talk at IISER Kolkata, May 28, 2023)
  • The Math behind the Chat (GPT)(Virtual talk at IISER Kolkata, June 28, 2023)

    Research Interests

    Number Theory: Artin's conjecture, Elliptic curves, Modular Forms, Automorphic forms, Langlands Program, Selberg's conjectures, Sieve Methods, Cryptography
    More research description can be found at CICMA
  • Here is chronological list of mathematical publications: LIST
  • Here is the list of philosophical publications: LIST
  • This is the link for Mathematical Reviews of my papers.
  • Here is the link to my mathematical genealogy.

    Degrees and Honours

    Expository Lectures

  • The Art of Research, 2005 Herzberg Lecture, Carleton University/Tata Institute for Fundamental Research, Mumbai, India.
  • Ellipses and elliptic curves, Coleman-Ellis Lecture, March 30, 2006.
  • Recent Developments in the Langlands Program, C.R. Math. Acad. Sci. R. Can., 24(2002), no. 2, 33-54.
  • A Motivated Introduction to the Langlands Program, in Advances in Number Theory, (edited by F. Gouvea and N. Yui), pp. 37-66, Clarendon Press, Oxford, 1993.
  • Ramanujan graphs, Journal of the Ramanujan Math. Society, 18, No. 1, (2003), 1-20.
  • Selberg's conjectures and Artin L-functions, Bulletin of the American Math. Society, 31(1) (1994), 1-14.

    Recent Publications

  • Sudoku squares and chromatic polynomials(with A. Herzberg), Notices of the Amer. Math. Society, 54(2007), no. 6, 708-717.
  • 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.
  • An introduction to sieve methods and their applications, (with A. Cojocaru) London Mathematical Society Student Texts, 66, Cambridge University Press, 2006.
  • Problems in Analytic Number Theory, Graduate Texts in Mathematics, Vol. 206, Springer-Verlag, 2001.
  • Lectures on Symmetric Power L-functions (Fields Institute, 2004)(pdf format)
  • Problems in Algebraic Number Theory, (with J. Esmonde), Graduate Texts in Mathematics, 190, Springer-Verlag, 2005, 2nd edition.
  • Non-vanishing of L-functions and Applications, Progress in Mathematics 157, Birkhauser, 1997 (Balaguer Prize Monograph), (with Vijaya Kumar Murty)
  • Spectral Estimates for Abelian Cayley Graphs, (with J. Friedman and J-P. Tillich), Journal of Combinatorial Theory, Series B., 96(2006), no. 1, 111-121.
  • The square sieve and the Lang-Trotter conjecture (with A. Cojocaru and E. Fouvry), Canadian Journal of Math., 57(6) (2005), 1155-1177.
  • Sieve methods in combinatorics (with Y.-R. Liu), Journal of Combinatorial Theory, Series A, 111(2005), no. 1, 1-23.
  • On decimations of l-sequences(with M. Goresky, A. Klapper, and I. Shparinski), SIAM Journal of Discrete Mathematics, 18 (2004), no. 1, 130-140.
  • Euclidean rings of algebraic integers (with M. Harper), Canadian Journal of Mathematics, 56(2004), no. 1, 71-76.
  • Cyclicity of elliptic curves modulo p and elliptic analogues of Linnik's problem, (with A. Cojocaru), Math. Annalen, 330 (2004), no. 3, 601-625.
  • On a conjecture of Birch and Swinnerton-Dyer (with W. Kuo), Canadian Journal of Math., 57(2005), no. 2, 328-337.
  • An application of Mumford's gap principle, (with J.J. Lee), Journal of Number Theory, 105(2004), no. 2, 333-343.

    Current Post-Doctoral Fellows:

    Abhishek Bharadwaj, David Nguyen, Sunil Naik.

    Current Doctoral Students:

    Nicolo Fellini, Becca Carter.

    Theses supervised:

    1. Ian Miyamoto, Primes and elliptic curves, M.Sc. thesis, McGill University, 1988.
    2. David Clark, L-series and ranks of elliptic curves, M.Sc. thesis, McGill University, 1988. (clark@math.byu.edu)
    3. David Clark, The Euclidean algorithm for Galois extensions of the rational numbers, Ph.D. thesis, McGill University, 1992.(clark@math.byu.edu)
    4. Tomasz Stefanicki, Non-vanishing of L-functions attached to automorphic representations of GL(2), Ph.D. thesis, McGill University, 1992.
    5. Francesco Pappalardi, On Artin's conjecture for primitive roots, Ph.D. thesis, McGill University, 1993. (pappa@mat.uniroma3.it)
    6. Chantal David, Supersingular Drinfeld modules, Ph.D. thesis, McGill University, 1993. (chantal@discrete.concordia.ca)
    7. Ashwaq Hashim, Application of Lindelof hypothesis to cusp forms, M.Sc. thesis, McGill University, 1993. (ucakash@ucl.ac.uk)
    8. Yuanli Zhang, Some analytic properties of automorphic L-functions, Ph.D. thesis, McGill University, 1994.(yz@math.purdue.edu)
    9. Sridhar Narayanan, Selberg's conjectures, M.Sc. thesis, McGill University, 1994.(sri@esankya.com)
    10. Keldon Drudge, The ABC Conjecture, M.Sc. Thesis, McGill University, 1995.
    11. Minatsu Yamaji, Applications of Brauer Induction to Artin L-functions, M.Sc. Thesis, McGill University, 1996.
    12. Francesco Sica, The order of vanishing of L-functions at the center of the critical strip, Ph.D. thesis, McGill University, 1998.
    13. Satya Mohit, The Wieferich criterion, the ABC conjecture and Shimura's correspondence, M.Sc. thesis, Queen's University, 1998.
    14. Yu-Ru Liu, The Turan sieve and some of its applications, M.Sc. thesis, Queen's University, 1998.(yrliu@math.harvard.edu)
    15. Filip Saidak, On conjectures about the distribution of primes in various sequences, M.Sc. thesis, Queen's University, 1998.(filips@math.ucalgary.ca)
    16. Malcolm Harper (PhD, McGill), A proof that $Z[\sqrt{14}]$ is Euclidean, Ph.D. thesis, McGill University, 2000.
    17. Steven Pope, On Problems of Cryptography: Primality testing and Factoring integers, M.Sc. thesis, Queen's University, 2000.
    18. Filip Saidak, On non-abelian generalizatons of the Erdös-Kac theorem, Ph.D. thesis, Queen's University, 2001.
    19. Alina Cojocaru, Cyclicity of Elliptic Curves modulo p, Ph.D. thesis, Queen's University, 2002.
    20. Kaneenika Sinha, Generalized Hurwitz zeta functions, (MSc, Queen's, 2002).
    21. Talia Borodin, Primality Testing and Factoring, (M.Sc., Queen's, 2003).
    22. Benjamin Ju, Elementary Proofs of the Prime Number Theorem, (M.Sc., Queen's, 2003).
    23. Tim Wotherspoon, Analysis of the Narayana-Fermat Factoring Algorithm(M.Sc., Queens, 2004).
    24. Jeanine Van Order, Counting Integral Ideals in an Algebraic Number Field,(M.Sc., Queen's, 2005).
    25. Sebastian Cioaba, Eigenvalues, Expanders and Gaps between Primes, (Ph.D., Queen's, 2005).
    26. Kaneenika Sinha, Effective Equidistribution of Eigenvalues of Hecke Operators, (Ph.D., Queen's, 2006).
    27. Brandon Fodden, Diophantine equations and the Generalized Riemann hypothesis (Ph.D., Queen's, 2007).
    28. Marilyn Reece Myers, Variations of Kummer's Conjecture (Ph.D., Queen's, 2007).
    29. Chester Weatherby, Transcendence of various infinite series and applications of Baker's theorem (Ph.D., Queen's, 2009).
    30. Robert Rundle, Generalized Pythagorean Triples (M.Sc., Queen's, 2007).
    31. Adam Felix, The order of a mod p and Artin's conjecture(M.Sc., Queen's, 2007).
    32. Andrew Droll, Properties of Ramanujan graphs (M.Sc., Queen's, 2008).
    33. Marc Papais, Graph spectra and the Ihara zeta function: implications and connections (M.Sc., Queen's, 2008).
    34. Carpio Cheng, Grimm's conjecture and a Gaussian analogue, (M.Sc. Queen's, 2009).
    35. Adam Felix,, Variations on Artin's primitive root conjecture (Ph.D., Queen's, 2011)
    36. Robert Rundle, Generalization of Ruderman's problem to imaginary quadratic fields (Ph.D., Queen's, 2012)
    37. Andrew Droll,, Variations of Li's criterion for an extension of the Selberg class (Ph.D., Queen's, 2012).
    38. Ryan Case, Ramanujan-Fourier series and applications (M.Sc., Queen's, 2013).
    39. Hector Pasten, Arithmetic problems around the abc conjecture and connections with logic, (Ph.D., Queen's, 2014).
    40. Siddhi Pathak, The Chowla problem and its generalizations, (M.Sc., Queen's, 2015)
    41. Kannappan Sampath , The saddle point method and its applications to number theory(M.Sc., Queen's, 2015)
    42. Akshaa Vatwani, Higher rank sieves and applications(Ph.D., Queen's, 2016).
    43. Arpita Kar, Representation of numbers by quaternary quadratic forms, (M.Sc. Queen's, 2016).
    44. Peng-Jie Wong, Character theory and Artin L-functions (Ph.D., Queen's, 2017).
    45. Francois Seguin, The two-variable Artin conjecture and elliptic analogues (Ph.D., Queen's, 2018)
    46. Siddhi Pathak, Special values of L-series, periodic coefficients, and related themes (Ph.D., Queen's, 2019).
    47. Christopher Zajner, An Encounter between East and West: The notion of truth in William James and Swami Vivekananda (M.A. Philosophy, Queen's, 2020).
    48. Paul Wilson, Lattices, codes and sphere packing problems (M.Sc., Queen's, 2020).
    49. Arpita Kar, Normal order of certain arithmetic functions and new analogues of the Erdos-Kac theorem (Ph.D., Queen's, 2020).
    50. Benoit Urvari, Cicero's Search for Yoga, (M.A. Philosophy, Queen's, 2022).