The doubling archimedean zeta integrals for unitary groups

Abstract: In order to verify the compatibility between the conjecture of Coates--Perrin-Riou and the interpolation results of the $p$-adic $L$-functions constructed by using the doubling method, a doubling archimedean zeta integral needs to be calculated for holomorphic discrete series. When the holomorphic discrete series is of scalar weight, it has been done by Bocherer-Schmidt and Shimura. In this talk, I will explain a way to compute this archimedean zeta integral for unitary groups of arbitrary signatures and general vector weights. This is a joint work with Ellen Eischen.

number theory

Audience: researchers in the topic

UCLA Number Theory Seminar