How to Verify the Riemann Hypothesis

TL;DR

This paper proposes a novel approach to verify the Riemann Hypothesis by analyzing a specific integral involving the xi function, aiming to establish its truth or falsehood.

Contribution

It introduces a new integral-based method for testing the Riemann Hypothesis, connecting the hypothesis to the properties of the xi function.

Findings

Proposes a specific integral as a test for the Riemann Hypothesis

Links the hypothesis validity to the behavior of the integral involving xi functions

Suggests potential for a new verification framework

Abstract

It is proposed that the validity, or not, of the Riemann Hypothesis might be established on the basis of the integral $$\int\frac{\xi(2s)}{\xi(s)}ds$$ where $$\xi(s)=(s-1)\pi^{-s/2}\Gamma(1+s/2)\zeta(s).$$