Moments of zeta and correlations of divisor-sums: stratification and Vandermonde integrals

TL;DR

This paper refines a heuristic for the Riemann zeta-function's shifted moments, deriving a new integral formula that parallels recent results for random matrix characteristic polynomial moments.

Contribution

It introduces a novel integral expression for the conjectured asymptotics of zeta moments, connecting number theory with random matrix theory.

Findings

New integral expression for zeta moments

Connection between zeta moments and random matrix theory

Refinement of previous heuristic models

Abstract

We refine a recent heuristic developed by Keating and the second author. Our improvement leads to a new integral expression for the conjectured asymptotic formula for shifted moments of the Riemann zeta-function. This expression is analogous to a formula, recently discovered by Brad Rodgers and Kannan Soundararajan, for moments of characteristic polynomials of random matrices from the unitary group.