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

Abstract

In this paper, we obtain upper bounds for the second moment of $L(u_j\times \varphi ,\frac{1}{2}+i{t}_j)$, where $\varphi$ 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 Lindelöf hypothesis. Previously these types of upper bounds are available for only $GL(n)\times GL(2)$, where $n\le 3.$

arXiv comment35 pages

References in corpus (2)

• A general Voronoi summation formula for GL(n,Z)
• The sixth moment of automorphic $L$-functions