English

Local integral transforms and global spectral decomposition

Number Theory 2025-09-16 v2

Abstract

We establish an explicit global spectral decomposition of shifted convolution sums and the second moment of automorphic LL-functions for Maass forms with explicit integral transforms as well as explicit inversion formulae over every local field.

Keywords

Cite

@article{arxiv.2404.10692,
  title  = {Local integral transforms and global spectral decomposition},
  author = {Valentin Blomer and Subhajit Jana and Paul D. Nelson},
  journal= {arXiv preprint arXiv:2404.10692},
  year   = {2025}
}

Comments

Minor update, to appear in Geom. Funct. Anal. (GAFA)

R2 v1 2026-06-28T15:56:02.848Z