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

2025/07/12 by Wu, Han
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2507.09125

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 side is nearly the characteristic function of a short family. Our method works for any tempered representation Π of PGL₃, and reveals the structural reason for the appearance of Katz's hypergeometric sums in a previous joint work with P.Xi.

Citations

• The cubic moment of L-functions for specified local component families
• On A Generalization of Motohashi's Formula
• A uniform Weyl bound for L-functions of Hilbert modular forms
• A double character sum of Conrey-Iwaniec and Petrow-Young
• On Weyl's Subconvex Bound for Cube-Free Hecke characters: Totally Real Case
• Eisenstein series and the cubic moment for PGL(2)

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