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arXiv · 1904.02025

Voronoï summation via switching cusps

Edgar Assing·Andrew Corbett
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Abstract

We consider the Fourier expansion of a Hecke (resp.\ Hecke--Maaß) cusp form of general level $N$ at the various cusps of $Γ_{0}(N)\bs\Hb$. We explain how to compute these coefficients via the local theory of $p$-adic Whittaker functions and establish a classical Voronoï summation formula allowing an arbitrary additive twist. Our discussion has applications to bounding sums of Fourier coefficients and understanding the (generalised) Atkin--Lehner relations.

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Edgar Assing, Andrew Corbett. 2019-04-03. Voronoï summation via switching cusps. https://arxiv.org/abs/1904.02025

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