English

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}
}
R2 v1 2026-06-28T19:21:51.607Z