The second moment of Dirichlet twists of a text {GL}_{4} automorphic L-function

Abstract

In this paper, we give an asymptotic formula for the second moment of Dirichlet twists of an automorphic L-function L(s, pi ) on the critical line averaged over characters and conductors, where pi denotes an irreducible tempered cuspidal automorphic representation of {textrm{GL}}_{4}({mathbb {A}}_{mathbb {Q}}) with unitary central character. We give some hybrid bound for the error term with respect to the size of conductors of Dirichlet characters and that of the automorphic representation.