Brian Conrey

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20242026

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math.NT2026

Critical Zeros and Unconditional Mean Value Theorems for twisted $PGL (2)$ and $PGL (3)$ $L$ -functions

Brian Conrey, Chung-Hang Kwan, Yongxiao Lin +1

Let $Π_{0}$ be a cuspidal automorphic representation of $PGL_{3} (A_{Q})$ . In this paper, we use Levinson's method to prove that, as $Q \to \infty$ , at lea…

math.NT2025

Twisted moments of characteristic polynomials of random matrices in the unitary group

Siegfred Baluyot, Brian Conrey

Recently, Keating and the second author of this paper devised a heuristic for predicting asymptotic formulas for moments of the Riemann zeta-function $ζ (s)$ . Their approach indicat…

math.NT2024

Character Sums and the Riemann Hypothesis

Brian Conrey

We prove that an innocent looking inequality implies the Riemann Hypothesis and show a way to approach this inequality through sums of Legendre symbols.

Critical Zeros and Unconditional Mean Value Theorems for twisted PGL(2) and PGL(3) L-functions

Twisted moments of characteristic polynomials of random matrices in the unitary group

Character Sums and the Riemann Hypothesis

Critical Zeros and Unconditional Mean Value Theorems for twisted $PGL (2)$ and $PGL (3)$ $L$ -functions