Equidistribution Rates, Closed String Amplitudes, and the Riemann Hypothesis

TL;DR

This paper links the Riemann hypothesis to equidistribution rates of automorphic forms and explores their implications for closed string amplitudes, offering a novel perspective on a longstanding mathematical conjecture.

Contribution

It reformulates the Riemann hypothesis through automorphic form equidistribution rates and connects these to closed string amplitude computations.

Findings

Reformulation of the Riemann hypothesis in terms of equidistribution convergence rates.

Establishment of a connection between number theory and string theory.

Potential new approaches to testing the Riemann hypothesis via string theory.

Abstract

We study asymptotic relations connecting unipotent averages of $Sp(2g,\mathbb{Z})$ automorphic forms to their integrals over the moduli space of principally polarized abelian varieties. We obtain reformulations of the Riemann hypothesis as a class of problems concerning the computation of the equidistribution convergence rate in those asymptotic relations. We discuss applications of our results to closed string amplitudes. Remarkably, the Riemann hypothesis can be rephrased in terms of ultraviolet relations occurring in perturbative closed string theory.