%0 Journal Article
%T The second moment of Dirichlet twists of Hecke $L$-functions
%A Peng Gao
%A Rizwanur Khan
%A Guillaume Ricotta
%J Mathematics
%D 2008
%I arXiv
%R 10.4064/aa140-1-4
%X Fix a Hecke cusp form $f$, and consider the $L$-function of $f$ twisted by a primitive Dirichlet character. As we range over all primitive characters of a large modulus $q$, what is the average behavior of the square of the central value of this $L$-function? Stefanicki proved an asymptotic valid only for $q$ having very few prime factors, and we extend this to almost all $q$.
%U http://arxiv.org/abs/0812.2606v2