Functional Mellin and Zeta Zeros

TL;DR

This paper introduces a theorem involving functional Mellin transforms that generalizes a fundamental matrix exponential-trace/determinant relationship and explores its implications for the Riemann hypothesis, leveraging zeta function symmetries.

Contribution

It presents a new theorem in the context of functional Mellin transforms that could provide a novel approach to understanding the Riemann hypothesis.

Findings

Generalizes the relationship between exponential trace and determinant using functional Mellin transforms.

Highlights the involution symmetry of the zeta function as a potential tool for the Riemann hypothesis.

Suggests a new strategy for approaching the Riemann hypothesis based on the theorem.

Abstract

A key theorem formulated in the context of functional Mellin transforms generalizes the important relationship $\exp\mathrm{tr} M=\det\exp M$. Along with the involution symmetry of the zeta function, the theorem suggests a strategy for tackling the Riemann hypothesis.