The sixth moment of automorphic L-functions

Chandee, Vorrapan; Li, Xiannan

doi:10.2140/ant.2017.11.583

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The sixth moment of automorphic $L$-functions

Vorrapan Chandee and Xiannan Li

Vol. 11 (2017), No. 3, 583–633

DOI: 10.2140/ant.2017.11.583

Abstract

We consider the $L$ -functions $L (s, f)$ , where $f$ is an eigenform for the congruence subgroup $Γ_{1} (q)$ . We prove an asymptotic formula for the sixth moment of this family of automorphic $L$ -functions.

Keywords

moment of $L$-functions, automorphic $L$-functions, $\Gamma_1(q)$

Mathematical Subject Classification 2010

Primary: 11M41

Secondary: 11F11, 11F67

Milestones

Received: 16 February 2016

Revised: 25 July 2016

Accepted: 16 December 2016

Published: 6 May 2017

Authors

Vorrapan Chandee
Department of Mathematics Burapha University 169 Long-Hard Bangsaen rd Saensuk Mueng 20131 Thailand

Xiannan Li
Department of Mathematics Kansas State University 138 Cardwell Hall Manhattan, KS 66506 United States

Vol. 11, No. 3, 2017