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

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.

2 Figures. Differences to version 1. There are several improvments in the presentation, including a better fitting title and abract. We also have corrected some minor mathematical errors