Equidistribution Rates, Closed String Amplitudes, and the Riemann Hypothesis

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.

15 pages

References in corpus (12)

• Two-Loop Superstrings I, Main Formulas
• Two-Loop Superstrings II, The Chiral Measure on Moduli Space
• Two-Loop Superstrings IV, The Cosmological Constant and Modular Forms
• Two-Loop Superstrings III, Slice Independence and Absence of Ambiguities
• Modular Forms and Three Loop Superstring Amplitudes
• Asyzygies, modular forms, and the superstring measure II
• Superstring scattering amplitudes in higher genus
• Asyzygies, modular forms, and the superstring measure I
• Two loop superstring amplitudes and S_6 representations
• NSR Superstring Measures Revisited
• Genus four superstring measures
• A novel method for computing torus amplitudes for ${\mathbb{Z}}_N$ orbifolds without the unfolding technique

Cited by in corpus (4)

• Will a physicist prove the Riemann Hypothesis?
• Vacuum stability, string density of states and the Riemann zeta function
• From Veneziano to Riemann: A String Theory Statement of the Riemann Hypothesis
• Eluding SUSY at every genus on stable closed string vacua