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arXiv · 2111.05406

The second moment of $GL(4) \times GL(2)$ $L$-functions at special points

Vorrapan Chandee·Xiannan Li
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Abstract

In this paper, we obtain upper bounds for the second moment of $L(u_j \times \phi, \frac{1}{2} + it_j)$, where $\phi$ is a Hecke Maass form for $SL(4, \mathbb Z)$, and $u_j$ is taken from an orthonormal basis of Hecke-Maass forms on $SL(2, \mathbb{Z})$ with eigenvalue $1/4 + t_j^2$. The bounds are consistent with the Lindel\"{o}f hypothesis. Previously these types of upper bounds are available for only $GL(n) \times GL(2)$, where $n \leq 3.$

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Vorrapan Chandee, Xiannan Li. 2021-11-09. The second moment of $GL(4) \times GL(2)$ $L$-functions at special points. https://arxiv.org/abs/2111.05406

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