One-level density of quadratic twists of $L$-functions

TL;DR

This paper studies the distribution of low-lying zeros of quadratic twists of automorphic L-functions, providing improved results under certain hypotheses by leveraging functional equations for quadratic Dirichlet L-functions.

Contribution

It introduces new bounds on the one-level density of zeros using only functional equations, advancing understanding of zero distributions without relying on more complex assumptions.

Findings

Enhanced bounds on zero distribution under GRH and Ramanujan-Petersson conjecture

Utilized functional equations to improve previous results

Applicable to quadratic twists of automorphic L-functions

Abstract

In this paper, we investigate the one-level density of low-lying zeros of quadratic twists of automorphic $L$-functions under the generalized Riemann hypothesis and the Ramanujan-Petersson conjecture. We improve upon the known results using only functional equations for quadratic Dirichlet $L$-functions.