From Veneziano to Riemann: A String Theory Statement of the Riemann Hypothesis

TL;DR

This paper explores a novel connection between string theory's Veneziano amplitude and the Riemann hypothesis, relating zeta function ratios to integral criteria and offering a physical perspective on the conjecture.

Contribution

It establishes a precise relation between string theory amplitudes and the Riemann hypothesis, introducing a generalized integral criterion and linking it to existing mathematical conditions.

Findings

Derived a relation between Veneziano amplitude and zeta function ratios.

Connected integral criteria for the Riemann hypothesis with string theory concepts.

Proposed a new generalization of the integral criterion for the hypothesis.

Abstract

We discuss a precise relation between the Veneziano amplitude of string theory, rewritten in terms of ratios of the Riemann zeta function, and two elementary criteria for the Riemann hypothesis formulated in terms of integrals of the logarithm and the argument of the zeta function. We also discuss how the integral criterion based on the argument of the Riemann zeta function relates to the Li criterion for the Riemann hypothesis. We provide a new generalization of this integral criterion. Finally, we comment on the physical interpretation of our recasting of the Riemann hypothesis in terms of the Veneziano amplitude.