On the Physics of the Riemann Zeros

TL;DR

This paper explores a formal integral expression for Li coefficients linked to the Riemann xi-function, suggesting positivity criteria and a potential physical interpretation within the Hilbert-Polya framework, and discusses connections to string theory.

Contribution

It introduces a new integral expression for Li coefficients that does not rely on the Riemann Hypothesis and proposes a physical perspective involving string theory.

Findings

Positivity of Li coefficients implies zeros are on the critical line

Proposes a physical interpretation via Hilbert-Polya approach

Suggests a relation between string theory and the Riemann Hypothesis

Abstract

We discuss a formal derivation of an integral expression for the Li coefficients associated with the Riemann xi-function which, in particular, indicates that their positivity criterion is obeyed, whereby entailing the criticality of the non-trivial zeros. We conjecture the validity of this and related expressions without the need for the Riemann Hypothesis and discuss a physical interpretation of this result within the Hilbert-Polya approach. In this context we also outline a relation between string theory and the Riemann Hypothesis.