Abstract
We study an exponential sum over Laplacian eigenvalues of Maaß forms on \(\varGamma \backslash {\mathbb {H}}\), where \(\varGamma \) is a congruence subgroup of \({{\,\mathrm{SL}\,}}_{2}({\mathbb {Z}})\) and \({\mathbb {H}}\) 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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The author acknowledges the support of the Masason Foundation and the Spirit of Ramanujan STEM Talent Initiative.
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Kaneko, I. Spectral exponential sums on hyperbolic surfaces. Ramanujan J 60, 837–846 (2023). https://doi.org/10.1007/s11139-022-00620-1
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DOI: https://doi.org/10.1007/s11139-022-00620-1