Towards a spectral proof of Riemann's hypothesis

TL;DR

This paper explores a spectral approach to Riemann's hypothesis by linking the xi function to the spectral properties of a magnetic Laplacian on a specific geometric surface.

Contribution

It proposes a novel spectral interpretation of the Riemann xi function as a characteristic function of a magnetic Laplacian with particular boundary and geometric conditions.

Findings

Evidence linking xi function to magnetic Laplacian spectrum

Potential geometric model for Riemann's hypothesis

New perspective on spectral proof approach

Abstract

The paper presents evidence that Riemann's xi function evaluated at 2 sqrt(E) could be the characteristic function P(E) for the magnetic Laplacian minus 85/16 on a surface of curvature -1 with magnetic field 9/4, a cusp of width 1, a DIrichlet condition at a point, and other conditions not yet determined.