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 ${\text{GL}}_4$ 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.

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References in corpus (1)

• The sixth moment of automorphic $L$-functions