Further Comments on Realization of Riemann Hypothesis via Coupling Constant Spectrum

TL;DR

This paper discusses a mathematical approach to the Riemann Hypothesis using the coupling constant spectrum of a quantum mechanical system, providing theoretical confirmation of previous results.

Contribution

It applies Carlson's theorem to validate earlier findings that connect the Riemann Hypothesis with the spectral properties of a quantum system involving inverse-square potential.

Findings

Confirmation of the Riemann Hypothesis via spectral analysis

Application of Carlson's theorem to quantum spectral problems

Theoretical validation of previous spectral approach results

Abstract

We invoke Carlson's theorem to justify and to confirm the results previously obtained on the validity of Riemann Hypothesis via the coupling constant spectrum of the zero energy S-wave Jost function a la N. N. Khuri, for the real, repulsive inverse-square potential in non-relativistic quantum mechanics in 3 dimensions.