Contributions to the study of the non-trivial roots of the Riemann zeta-function

TL;DR

This paper explores the non-trivial roots of the Riemann zeta function by constructing self-adjoint operators, aiming to provide insights aligned with the Hilbert-Polya conjecture.

Contribution

It introduces a series of self-adjoint operators on a Hilbert space whose eigenvalues approximate the non-trivial roots of the zeta function, advancing the spectral approach to the Riemann hypothesis.

Findings

Constructed operators whose eigenvalues approximate zeta roots

Provides a new spectral perspective on the Riemann hypothesis

Supports the Hilbert-Polya conjecture framework

Abstract

This work contributes to the study of the non-trivial roots of the Riemann zeta function. In view of the Hilbert-Polya conjecture a series of self-adjoint operators on a Hilbert space is constructed whose eigenvalues approximate these roots.