The asymptotic representation of some series and the Riemann hypothesis

TL;DR

This paper proposes a conjecture about the asymptotic behavior of specific series that, if true, would imply the Riemann hypothesis and suggest the simplicity of the zeta-function's non-trivial zeros.

Contribution

It introduces a new conjecture linking series asymptotics to the Riemann hypothesis and properties of zeta zeros.

Findings

Conjecture implies the Riemann hypothesis

Suggests simplicity of non-trivial zeros

Provides a new perspective on zeta-function zeros

Abstract

We present a conjecture about the asymptotic representation of certain series. The conjecture implies the Riemann hypothesis and it would also indicate the simplicity of the non-trivial zeros of the zeta-function.