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arXiv · 1411.4541

A mean value of a triple product of $L$-functions

Jack Buttcane·Rizwanur Khan
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Abstract

Luo has proven an optimal upper bound for the $L^4$-norm of dihedral Maass forms of large eigenvalue, by bounding a mean value of triple product $L$-functions. Motivated by this result, we study a mean value of $L$-functions having similar shape, and obtain for it an asymptotic with power savings. Our work may be helpful in eventually obtaining an asymptotic for the $L^4$-norm.

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Jack Buttcane, Rizwanur Khan. 2014-11-17. A mean value of a triple product of $L$-functions. https://arxiv.org/abs/1411.4541

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