Vorono\"{i} summation via switching cusps
Number Theory
2019-04-04 v1
Abstract
We consider the Fourier expansion of a Hecke (resp.\ Hecke--Maa\ss) cusp form of general level at the various cusps of . We explain how to compute these coefficients via the local theory of -adic Whittaker functions and establish a classical Vorono\"i summation formula allowing an arbitrary additive twist. Our discussion has applications to bounding sums of Fourier coefficients and understanding the (generalised) Atkin--Lehner relations.
Keywords
Cite
@article{arxiv.1904.02025,
title = {Vorono\"{i} summation via switching cusps},
author = {Edgar Assing and Andrew Corbett},
journal= {arXiv preprint arXiv:1904.02025},
year = {2019}
}