Character sum, reciprocity and Voronoi formula
Number Theory
2025-01-22 v2
Abstract
We prove a novel four-variable character sum identity which serves as a twisted, non-archimedean counterpart to Weber's integrals for Bessel functions. Using this identity and ideas from Venkatesh's thesis, we present a new, spectral proof of the Voronoi formula for classical modular forms.
Cite
@article{arxiv.2410.11193,
title = {Character sum, reciprocity and Voronoi formula},
author = {Chung-Hang Kwan and Wing Hong Leung},
journal= {arXiv preprint arXiv:2410.11193},
year = {2025}
}