A Weyl Creation Algebra Approach to the Riemann Hypothesis

TL;DR

This paper proposes a novel approach to the Riemann Hypothesis using Weyl creation operators and ergodic theory, connecting quantum mechanics concepts to analyze zeta functions and potentially resolve the conjecture.

Contribution

It introduces a Weyl creation algebra framework combined with ergodic theory to study the Riemann Hypothesis, offering a new perspective on the problem.

Findings

Finite Hasse-Dirichlet eta functions can be derived from creation operators

Complex quantum mechanics concepts are applied to number theory

Potential pathway to settle RH through Euler factor analysis

Abstract

We sketch a Weyl creation operator approach to the Riemann Hypothesis; i.e.,arithmetic on the Weyl algebras with ergodic theory to transport operators. We prove that finite Hasse-Dirichlet alternating zeta functions or eta functions can be induced from a product of "creation operators". The latter idea is the result of considering complex quantum mechanics with complex time-space related concepts. Then we overview these ideas, with variations, which may provide a pathway that may settle RH; e.g., a Euler Factor analysis to study the quantum behavior of the integers as one pushes up the critical line near a macro zeta function zero.