On signs of coefficients of L-functions

TL;DR

This paper establishes a general lower bound on how often the real coefficients of L-functions change sign, extending known results for certain groups and providing new bounds for others.

Contribution

It introduces a unified approach to bound sign changes of L-function coefficients across different groups, including new results for GSp(4).

Findings

Established a general lower bound for sign changes.

Recovered known results for GL(2) and GL(3).

Derived new bounds for GSp(4).

Abstract

We give a general lower bound on the frequency of sign changes in the real coefficients of L-functions of the Selberg class. We in particular recover existing results in the cases of GL(2) and GL(3), and obtain new bounds in the case of GSp(4).