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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna


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Volume 29, Issue 3

Issues

The Selberg trace formula as a Dirichlet series

Andrew R. Booker / Min Lee
Published Online: 2016-07-12 | DOI: https://doi.org/10.1515/forum-2015-0256

Abstract

We explore an idea of Conrey and Li of expressing the Selberg trace formula as a Dirichlet series. We describe two applications, including an interpretation of the Selberg eigenvalue conjecture in terms of quadratic twists of certain Dirichlet series, and a formula for an arithmetically weighted sum of the complete symmetric square L-functions associated to cuspidal Maass newforms of squarefree level N>1.

Keywords: Selberg trace formula

MSC 2010: 11F72; 11F66; 11F41

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About the article


Received: 2015-12-18

Revised: 2016-05-10

Published Online: 2016-07-12

Published in Print: 2017-05-01


Funding Source: Engineering and Physical Sciences Research Council

Award identifier / Grant number: EP/H005188/1

Award identifier / Grant number: EP/L001454/1

Award identifier / Grant number: EP/K034383/1

Both authors were supported by EPSRC Grants EP/H005188/1, EP/L001454/1 and EP/K034383/1.


Citation Information: Forum Mathematicum, Volume 29, Issue 3, Pages 519–542, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2015-0256.

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