Level Reciprocity in the twisted second moment of Rankin-Selberg L-functions

Abstract

We prove an exact formula for the second moment of Rankin-Selberg $L$-functions $L(1/2,f\times g)$ twisted by ${\lambda }_f(p)$, where $g$ is a fixed holomorphic cusp form and $f$ is summed over automorphic forms of a given level $q$. The formula is a reciprocity relation that exchanges the twist parameter $p$ and the level $q$. The method involves the Bruggeman/Kuznetsov trace formula on both ends; finally the reciprocity relation is established by an identity of sums of Kloosterman sums.

13 pages

References in corpus (1)

• On the reciprocity law for the twisted second moment of Dirichlet $L$-functions

Cited by in corpus (6)

• The fourth moment of Dirichlet $L$-functions along a coset and the Weyl bound
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• Motohashi's Formula for the Fourth Moment of Individual Dirichlet $L$-Functions and Applications
• Mixed moment of $GL(2)$ and $GL(3)$ $L$-functions
• $L^p$-Norm Bounds for Automorphic Forms via Spectral Reciprocity