Will a physicist prove the Riemann Hypothesis?

TL;DR

This paper explores the Riemann Hypothesis by examining its number theoretical aspects and its connections to various physical systems, including random matrix theory and statistical mechanics.

Contribution

It provides a comprehensive review of the mathematical properties of the Riemann zeta function and its intriguing links to physical phenomena, highlighting interdisciplinary approaches.

Findings

Connections between the Riemann Hypothesis and Random Matrix Theory

Relation of the hypothesis to Lee--Yang zeros in statistical mechanics

Discussion of physical models like random walks and billiards

Abstract

In the first part we present the number theoretical properties of the Riemann zeta function and formulate the Riemann Hypothesis. In the second part we review some physical problems related to this hypothesis: the links with Random Matrix Theory, relation with the Lee--Yang theorem on the zeros of the partition function, random walks, billiards etc.