Riemann Hypothesis as an Uncertainty Relation

TL;DR

This paper introduces a Riemann operator that reformulates the Riemann hypothesis as a Heisenberg-type uncertainty relation, bridging number theory and quantum physics to offer a novel perspective on the zeros of the zeta function.

Contribution

It presents a new operator-based approach that transforms the Riemann hypothesis into an uncertainty relation, connecting physics concepts with number theory.

Findings

Riemann operator formulation of the hypothesis

Uncertainty relation equivalent to the Riemann hypothesis

Potential new avenues for analyzing zeta zeros

Abstract

Physics is a fertile environment for trying to solve some number theory problems. In particular, several tentative of linking the zeros of the Riemann-zeta function with physical phenomena were reported. In this work, the Riemann operator is introduced and used to transform the Riemann's hypothesis in a Heisenberg-type uncertainty relation, offering a new way for studying the zeros of Riemann's function