The Selberg trace formula as a Dirichlet series

Andrew R Booker; Min Lee

doi:10.1515/forum-2015-0256

The Selberg trace formula as a Dirichlet series

Andrew R Booker, Min Lee

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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287 Downloads (Pure)

Abstract

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

Original language	English
Pages (from-to)	519-542
Number of pages	24
Journal	Forum Mathematicum
Volume	29
Issue number	3
Early online date	12 Jul 2016
DOIs	https://doi.org/10.1515/forum-2015-0256
Publication status	Published - May 2017

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10.1515/forum-2015-0256

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This is the author accepted manuscript (AAM). The final published version (version of record) is available online via De Gruyter at http://dx.doi.org/10.1515/forum-2015-0256. Please refer to any applicable terms of use of the publisher.
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Persistent link

Detecting squarefree numbers
Booker, A. R.
1/07/13 → 1/07/15
Project: Research
Explicit number theory, automorphic forms and L-functions
Booker, A. R.
1/10/09 → 1/04/15
Project: Research

Professor Andrew R Booker
- Andrew.Bookerbristol.acuk
- School of Mathematics - Professor of Pure Mathematics
Person: Academic
Dr M Lee
- min.leebristol.acuk
- School of Mathematics - Lecturer and Royal Society University Research Fellow
- Pure Mathematics
Person: Academic , Member

Cite this

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title = "The Selberg trace formula as a Dirichlet series",

abstract = "We explore an idea of Conrey and Li of expressing the Selberg trace formula asa Dirichlet series. We describe two applications, including an interpretation of the Selbergeigenvalue conjecture in terms of quadratic twists of certain Dirichlet series, and a formulafor an arithmetically weighted sum of the complete symmetric square L-functions associatedto cuspidal Maass newforms of squarefree level N > 1.",

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

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DO - 10.1515/forum-2015-0256

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The Selberg trace formula as a Dirichlet series

Abstract

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Projects

Detecting squarefree numbers

Explicit number theory, automorphic forms and L-functions

Profiles

Professor Andrew R Booker

Dr M Lee

Cite this