Symmetries and the Riemann Hypothesis

TL;DR

This paper explores the connection between symmetries in classical semi-simple groups and their associated zeta functions, which are linked to the Riemann hypothesis, highlighting the role of Weyl group symmetries.

Contribution

It introduces a framework relating group symmetries to zeta functions associated with maximal parabolics, advancing understanding of their properties and the Riemann hypothesis.

Findings

Zeta functions linked to semi-simple groups exhibit symmetries similar to Riemann's zeta.

These symmetries include Weyl group actions, influencing the functions' properties.

The work suggests these zeta functions may satisfy the Riemann hypothesis under certain conditions.

Abstract

Associated to classical semi-simple groups and their maximal parabolics are genuine zeta functions. Naturally related to Riemann's zeta and governed by symmetries, including that of Weyl, these zetas are expected to satisfy the Riemann hypothesis.