Brad Rodgers @ QueensU
Publications and preprints
- Squarefrees are Gaussian in short intervals.
With O. Gorodetsky and A. Mangerel.
[arXiv]
- Moments of polynomials with random multiplicative coefficients. To appear, Mathematika.
With J. Benatar and A. Nishry.
[arXiv]
- On the variance of squarefree integers in short intervals and arithmetic progressions. Geom. Funct. Anal. 31 (2021), 111--149.
With O. Gorodetsky, K. Matomäki, and M. Radziwill.
[arXiv] [Journal]
- Sums of singular series and primes in short intervals in algebraic number fields.
With V. Kuperberg and E. Roditty-Gershon.
[arXiv]
- Traces of powers of matrices over finite fields. Trans. Amer. Math. Soc. 374 (2021), 4579--4638.
With O. Gorodetsky.
[arXiv] [Journal]
- Band-limited mimicry of point processes by point processes supported on a lattice. Ann. Appl. Probab. 31 (2021), no. 1, 351--376.
With J. Lagarias.
[arXiv] [Journal]
- Higher correlations and the alternative hypothesis. Q. J. Math. 71 (2020), no. 1, 257--280.
With J. Lagarias.
[arXiv] [Journal]
- The variance of the number of sums of two squares in \(\mathbb{F}_q[T]\) in short intervals. Amer. J. Math. 143 (2021), no. 6, 1703--1745
With O. Gorodetsky.
[arXiv] [Journal]
Code used for numerical graphs: [SAGE z-measures] [SAGE variance graphs][MATLAB progressions] [MATLAB intervals]
- The De Bruijn-Newman constant is non-negative. Forum Math. Pi 8 (2020).
With T. Tao.
[arXiv] [Journal]
- A limiting characteristic polynomial for classical matrix ensembles. Ann. Henri Poincare 20 (2019), 1093--1119.
With R. Chhaibi, E. Hovhannisyan, J. Najnudel, and A. Nikeghbali.
[arXiv] [Journal]
- The variance of divisor sums in arithmetic progressions. Forum Math. 30 (2018), no. 2, 269--293.
With K. Soundararajan.
[arXiv] [Journal]
- On the distribution of Rudin-Shapiro polynomials and lacunary walks on \(SU(2)\). Adv. Math. 320 (2017), 993--1008.
[arXiv] [Journal] [Corrections to published version: pdf]
- Arithmetic functions in short intervals and the symmetric group. Algebra Number Theory. 12 (2018), no. 5, 1243--1279.
[arXiv] [Journal]
- Sums of divisor functions in \(\mathbb{F}_q[t]\) and matrix integrals. Math. Z. 288 (2018), no. 1-2, 167--198.
With J. Keating, E. Roditty-Gershon, and Z. Rudnick.
[arXiv] [Journal]
- Tail bounds for counts of zeros and eigenvalues, and an application to ratios. Comment. Math. Helv. 92 (2017), no. 2, 311--347.
[arXiv] [Journal]
- Bootstrapped zero density estimates and a central limit theorem for the zeros of the zeta function. Int. J. Number Theory 11 (2015), no. 7, 2087--2107.
With Kenneth Maples.
[arXiv] [Journal]
- The covariance of almost-primes in \( \mathbb{F}_q[T]\). Int. Math. Res. Not. IMRN. 2015 (2015), no. 14, 5976--6004.
[arXiv] [Journal]
- Arithmetic consequences of the GUE conjecture for zeta zeros.
[PDF]
- A central limit theorem for the zeroes of the zeta function. Int. J. Number Theory 10 (2014), no. 2, 483--511.
[arXiv] [Journal] [Corrections to published version: pdf]
- Macroscopic pair correlation of the Riemann zeroes for smooth test functions. Q. J. Math. 64 (2013), no. 4, 1197--1219.
[arXiv] [Journal]
- The statistics of the zeros of the Riemann zeta-function and related topics. Ph.D. Thesis, University of California, Los Angeles. (2013) 228pp.
[Link]
Some talks with powerpoint slides
- Arithmetic functions in short intervals (JMM 17) [Slides]
- Explicit formulas and symmetric function theory. [Slides]
- The distribution of primes and almost-primes in short intervals. [Slides]
- The strong Szegő theorem in random matrix theory and number theory. [Slides]
- Statistics of the zeta zeros: mesoscopic and macroscopic phenomena. [Slides]
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