Realization of the Riemann Hypothesis via Coupling Constant Spectrum

TL;DR

This paper proposes a non-relativistic quantum mechanical model that connects the Riemann Hypothesis to the spectrum of a coupling constant, offering a novel physical approach to this longstanding mathematical conjecture.

Contribution

It introduces a quantum model where the Riemann zeta function is realized through the S-wave Jost function at zero energy, linking physics and number theory in a new way.

Findings

Establishes a connection between the Riemann $\xi(s)$ function and quantum scattering theory.

Provides a framework for analyzing the Riemann Hypothesis using quantum mechanical spectra.

Builds on Khuri's work to relate the Jost function to the Riemann zeta function.

Abstract

We present a Non-relativistic Quantum mechanical model, which exhibits the realization of Riemann Conjecture. The technique depends on exposing the $S$-wave Jost function at zero energy and in identifying it with the Riemann $\xi(s)$ function following a seminal paper of N. N. Khuri.