The eighth moment of the family of Γ₁(q)-automorphic L-functions

2017/08/28 by Vorrapan Chandee, Chandee, Vorrapan, Xiannan Li +1
Mathematics · #Analytic Number Theory Research #Advanced Mathematical Identities #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.1708.08410

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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