On mean values of mollifiers and L-functions associated to primitive   cusp forms
  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. 
Patrick K\"uhn, Nicolas Robles and Dirk Zeindler
math.NT