#### Vol. 11, No. 3, 2017

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The sixth moment of automorphic $L$-functions

### Vorrapan Chandee and Xiannan Li

Vol. 11 (2017), No. 3, 583–633
##### Abstract

We consider the $L$-functions $L\left(s,f\right)$, where $f$ is an eigenform for the congruence subgroup ${\Gamma }_{1}\left(q\right)$. 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