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arXiv · 1708.08410

The eighth moment of the family of $Γ_1(q)$-automorphic $L$-functions

Vorrapan Chandee·Xiannan Li
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Abstract

We prove a Lindelöf on average bound for the eighth moment of a family of $L$-functions attached to automorphic forms on $GL(2)$, the first time this has been accomplished. Previously, such a bound had been proven for the sixth moment for our family by Djanković and for a similar family by Young. Our proof rests on a new approach which overcomes the lack of perfect orthogonality in the family initially observed by Iwaniec and Xiaoqing Li.

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Vorrapan Chandee, Xiannan Li. 2017-08-28. The eighth moment of the family of $Γ_1(q)$-automorphic $L$-functions. https://arxiv.org/abs/1708.08410

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