Families of nearly ordinary Eisenstein series on unitary groups

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 (r,s) 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.