A new necessary and sufficient condition for the Riemann hypothesis

TL;DR

This paper introduces a novel necessary and sufficient condition for the Riemann hypothesis based on an order condition involving finite rational combinations of the zeta-function at even positive integers.

Contribution

It provides a new equivalent formulation of the Riemann hypothesis using rational combinations of zeta values at even integers, offering a potential new approach to the problem.

Findings

New necessary and sufficient condition for the Riemann hypothesis

Condition involves order relations of rational combinations of zeta values

Potential implications for understanding the distribution of zeros

Abstract

We give a new equivalent condition for the Riemann hypothesis consisting in an order condition for certain finite rational combinations of the values of the Riemann zeta-function at even positive integers.