On the smooth transfer for Guo-Jacquet relative trace formulae

TL;DR

This paper proves the existence of smooth transfer in Guo-Jacquet relative trace formulae over p-adic fields, which is crucial for extending Waldspurger's results on L-functions of GL_2.

Contribution

It establishes the smooth transfer for Guo-Jacquet relative trace formulae in the p-adic setting, advancing the understanding of relative trace formulae and their applications.

Findings

Proves smooth transfer exists for Guo-Jacquet trace formulae in p-adic case

Facilitates generalization of Waldspurger's results on L-functions

Provides foundational step for further research in automorphic forms

Abstract

We establish the existence of smooth transfer for Guo-Jacquet relative trace formulae in $p$-adic case. This kind of smooth transfer is a key step towards a generalization of Waldspurger's result on central values of L-functions of $GL_2$.