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

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 th...

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Bibliographic Details
Published inarXiv.org
Main Authors Andersen, Nickolas, Eren, Mehmet Kiral
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 18.01.2018
Subjects
Mathematics - Number Theory
Reciprocity
Sums
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1801.06089