English

On a Generalization of Motohashi's Formula: Non-archimedean Weight Functions

Number Theory 2025-07-15 v1

Abstract

This is a continuation of the adelic version of Kwan's formula. At non-archimedean places we give a bound of the weight function on the mixed moment side, when the weight function on the PGL3×PGL2\mathrm{PGL}_3 \times \mathrm{PGL}_2 side is nearly the characteristic function of a short family. Our method works for any tempered representation Π\Pi of PGL3\mathrm{PGL}_3, and reveals the structural reason for the appearance of Katz's hypergeometric sums in a previous joint work with P.Xi.

Keywords

Cite

@article{arxiv.2507.09125,
  title  = {On a Generalization of Motohashi's Formula: Non-archimedean Weight Functions},
  author = {Han Wu},
  journal= {arXiv preprint arXiv:2507.09125},
  year   = {2025}
}