Asymptotic analysis on a pseudo-Hermitian Riemann-zeta Hamiltonian

TL;DR

This paper analyzes a Hamiltonian linked to the Riemann zeta zeros using Fourier and WKB methods, revealing asymptotic eigenfunction behavior and highlighting open problems in momentum space formulation.

Contribution

It introduces an asymptotic analysis of a pseudo-Hermitian Riemann-zeta Hamiltonian, providing insights into eigenfunctions and identifying open challenges in eigenvalue problem formulation.

Findings

WKB analysis yields exact asymptotic eigenfunction behavior

Fourier analysis reveals open problems in momentum space formulation

Eigenvalues correspond to zeros of the Riemann zeta function

Abstract

The differential-equation eigenvalue problem associated with a recently-introduced Hamiltonian, whose eigenvalues correspond to the zeros of the Riemann zeta function, is analyzed using Fourier and WKB analysis. The Fourier analysis leads to a challenging open problem concerning the formulation of the eigenvalue problem in the momentum space. The WKB analysis gives the exact asymptotic behavior of the eigenfunction.