Brad Rodgers @ QueensU

• Large prime factors of well-distributed sequences.
With A. Bharadwaj.
[arXiv]


• On convergence of points to limiting processes, with an application to zeta zeros.
With J. Arias de Reyna.
[arXiv]


• Autocorrelations of characteristic polynomials for the Alternative Circular Unitary Ensemble. Glasg. Math. J. 66 (2024), no. 1, 51--64.
With H. S. Vallabhaneni.
[arXiv] [Journal]


• Averages of quadratic twists of long Dirichlet polynomials.
With B. Conrey.
[arXiv]


• Squarefrees are Gaussian in short intervals. J. Reine Angew. Math. 795 (2023), 1--44.
With O. Gorodetsky and A. Mangerel.
[arXiv] [Journal]


• Moments of polynomials with random multiplicative coefficients. Mathematika 68 (2022), no. 1, 191--216.
With J. Benatar and A. Nishry.
[arXiv] [Journal]


• 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. Ramanujan J. 58 (2022), no. 2, 291--317.
With V. Kuperberg and E. Roditty-Gershon.
[arXiv] [Journal]


• 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. To appear, Mich. Math. J.
[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]