Number Theory Seminar

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.