Supersymmetry and the Riemann zeros on the critical line

TL;DR

This paper introduces a supersymmetric quantum mechanical model that links the Riemann zeros on the critical line to the model's ground state energy, offering a novel approach to understanding these zeros.

Contribution

It constructs a supersymmetric quantum model where the Riemann zeros correspond to the model's ground state energy vanishing, providing a new perspective on the zeros' distribution.

Findings

Zeros on the critical line emerge from the ground state energy condition.

The model connects the Riemann zeta function to supersymmetric quantum mechanics.

Provides a potential framework for studying the Riemann Hypothesis.

Abstract

We propose a new way of studying the Riemann zeros on the critical line using ideas from supersymmetry. Namely, we construct a supersymmetric quantum mechanical model whose energy eigenvalues correspond to the Riemann zeta function in the strip $0< {\rm Re}\, s < 1$ (in the complex parameter space) and show that the zeros on the critical line arise naturally from the vanishing ground state energy condition in this model.