Orateur
Description
The Rankin–Selberg method is a classical approach for constructing integral representations of L-functions, facilitating their meromorphic continuation and the establishment of functional equations. In this talk, we present a novel perspective that interprets Rankin–Selberg integrals within the framework of double flag varieties of finite type. We introduce the concept of strongly tempered spherical varieties of Rankin–Selberg type and, leveraging the classification by He, Nishiyama, Ochiai, and Oshima, systematically identify all Rankin–Selberg integrals associated with these varieties. This framework enables a unified treatment of local zeta integrals and the gamma factors for this family. As an application, we can derive complete L-functions corresponding to these Rankin–Selberg integrals and establish local multiplicity formulas via the local relative trace formula for certain strongly tempered spherical varieties of Gan-Gross-Prasad type over p-adic fields.
