A probabilistic interpretation for central zeros of $L$-functions in the Selberg class

TL;DR

This paper establishes a probabilistic framework for understanding central zeros of $L$-functions in the Selberg class, linking the Riemann hypothesis to properties of infinitely divisible distributions.

Contribution

It introduces a novel probabilistic interpretation of central zeros, connecting the Riemann hypothesis to infinitely divisible distributions for the first time.

Findings

Central zeros have a probabilistic interpretation.

Riemann hypothesis is equivalent to a condition on infinitely divisible distributions.

Provides a new perspective on the distribution of zeros in $L$-functions.

Abstract

We show that central zeros of $L$-functions in the Selberg class have a probabilistic interpretation by stating an equivalence condition of the Riemann hypothesis for the $L$-functions in terms of infinitely divisible distributions.