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
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
Funding statement: Both authors were supported by EPSRC Grants EP/H005188/1, EP/L001454/1 and EP/K034383/1.
Acknowledgements
We thank Dorian Goldfeld and Peter Sarnak for helpful suggestions and corrections.
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