Riemann Zero Condition Off the Critical Line: A Matrix Formulation

TL;DR

This paper introduces a finite-dimensional matrix framework for analyzing the Riemann zeta function off the critical line, providing new tools for understanding its zeros in complex analysis.

Contribution

It presents a novel matrix formulation that extends the study of the Riemann zeta function beyond the critical line, offering a new approach for zero analysis.

Findings

Matrix framework for off-critical line zeros

Potential insights into Riemann hypothesis

New computational methods for zeta function

Abstract

We develop a finite-dimensional, symmetric matrix framework associated with the Riemann zeta function for complex arguments s with Real(s) unequal 1/2.