On the smooth transfer for Guo-Jacquet relative trace formulae

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 $G{L}_2$.

arXiv commentto appear in Compositio Mathematica

References in corpus (4)

• Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups
• Automorphic period and the central value of Rankin--Selberg L-function
• Generalized Harish-Chandra descent, Gelfand pairs and an Archimedean analog of Jacquet-Rallis' Theorem
• Periods and nonvanishing of central L-values for GL(2n)

Cited by in corpus (5)

• Periods and nonvanishing of central L-values for GL(2n)
• An infinitesimal variant of Guo-Jacquet trace formula II
• Endoscopy for unitary symmetric spaces
• An infinitesimal variant of Guo-Jacquet trace formula I: the case of $(G{L}_{2n,D},G{L}_{n,D}\times G{L}_{n,D})$
• A local trace formula for $p$-adic infinitesimal symmetric spaces: the case of Guo-Jacquet