Gaussian test functions and Jacquet-Rallis transfer

2025/08/18 by Mihatsch, Andreas, Sankaran, Siddarth, Yang, Tonghai
#11F27 #11F70 #22E50 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2508.12598

Abstract

We construct Gaussian test functions for the general linear side of the Jacquet-Rallis relative trace formula comparison. These are functions which are defined in terms of their orbital integrals and transfer to the compact unitary group. Our construction relies on the formalism of Kudla-Millson and simple geometric properties of symmetric spaces. In particular, it also provides an explicit formula in terms of the Howe operator.

Citations

• The Kudla-Millson form via the Mathai-Quillen formalism
• On the Arithmetic Fundamental Lemma conjecture over a general p-adic field
• The global Gan-Gross-Prasad conjecture for unitary groups: the endoscopic case
• Isolation of cuspidal spectrum, with application to the Gan--Gross--Prasad conjecture
• Weil representation and Arithmetic Fundamental Lemma
• Arithmetic diagonal cycles on unitary Shimura varieties
• Comparison of local spherical characters and the Ichino-Ikeda conjecture for unitary groups

Related

• On the geometric side of the Jacquet-Rallis relative trace formula
• Le transfert singulier pour la formule des traces de Jacquet-Rallis
• La variante infinitésimale de la formule des traces de Jacquet-Rallis pour les groupes unitaires
• Les formules des traces relatives de Jacquet-Rallis grossières
• Beyond endoscopy for the relative trace formula I: local theory