On mean values of mollifiers and L-functions associated to primitive cusp forms

TL;DR

This paper investigates the second moment of L-functions linked to primitive cusp forms using new mollifiers, leading to improved bounds on the zeros of these functions.

Contribution

It introduces a novel family of mollifiers extending previous work, enhancing the understanding of L-function zeros for primitive cusp forms.

Findings

Improved lower bounds on zeros of L-functions

Extended mollifier family for better analysis

Enhanced understanding of cusp form L-functions

Abstract

We study the second moment of the L-function associated to a holomorphic primitive cusp form of even weight perturbed by a new family of mollifiers. This family is a natural extension of the mollifers considered by Conrey and by Bui, Conrey and Young. As an application, we improve the current lower bound on critical zeros of holomorphic primitive cusp forms.