Criteria equivalent to the Riemann Hypothesis

TL;DR

This paper reviews several criteria equivalent to the Riemann Hypothesis, focusing on the Riesz and Báez-Duarte criteria, proving their equivalence, and supporting findings with computational data.

Contribution

It establishes the equivalence of the Riesz and Báez-Duarte criteria and provides computational evidence supporting these criteria.

Findings

Proved the equivalence of Riesz and Báez-Duarte criteria

Provided computational data supporting the criteria

Reviewed multiple criteria equivalent to the Riemann Hypothesis

Abstract

We give a brief overview of a few criteria equivalent to the Riemann Hypothesis. Next we concentrate on the Riesz and B{\'a}ez-Duarte criteria. We proof that they are equivalent and we provide some computer data to support them. It is not compressed to six pages version of the talk delivered by M.W. during the XXVII Workshop on Geometrical Methods in Physics, 28 June -- 6 July, 2008, Bia{\l}owie{\.z}a, Poland.