The Selberg trace formula as a Dirichlet series

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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 languageEnglish
Pages (from-to)519-542
Number of pages24
JournalForum Mathematicum
Issue number3
Early online date12 Jul 2016
Publication statusPublished - May 2017


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