Families of nearly ordinary Eisenstein series on unitary groups

Abstract

We use the doubling method to construct $p$-adic $L$-functions and families of nearly ordinary Klingen Eisenstein series from nearly ordinary cusp forms on unitary groups of signature $\left(r,s\right)$ and Hecke characters, and prove the constant terms of these Eisenstein series are divisible by the $p$-adic $L$-function, following earlier constructions of Eischen, Harris, Li, Skinner and Urban. We also make preliminary computations for the Fourier–Jacobi coefficients of the Eisenstein series. This provides a framework to do Iwasawa theory for cusp forms on unitary groups.