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Spectral exponential sums on hyperbolic surfaces

Kaneko, Ikuya (2022) Spectral exponential sums on hyperbolic surfaces. Ramanujan Journal . ISSN 1382-4090. doi:10.1007/s11139-022-00620-1. (In Press)

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We study an exponential sum over Laplacian eigenvalues of Maaß forms on Γ∖ℍ, where Γ is a congruence subgroup of SL₂(ℤ) and ℍ is the upper half-plane. The goal is to establish an asymptotic formula that expresses the spectral exponential sum in terms of an oscillatory main term, the von Mangoldt function and the Selberg zeta function.

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Kaneko, Ikuya0000-0003-4518-1805
Additional Information:The author acknowledges the support of the Masason Foundation and the Spirit of Ramanujan STEM Talent Initiative.
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Masason FoundationUNSPECIFIED
Spirit of Ramanujan STEM Talent InitiativeUNSPECIFIED
Record Number:CaltechAUTHORS:20220908-231236714
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:116696
Deposited By: Melissa Ray
Deposited On:08 Sep 2022 23:12
Last Modified:08 Sep 2022 23:15

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