Siegel Eisenstein series of degree n and Λ-adic Eisenstein series

Let F be a totally real field and χ a primitive narrow ray class character of F. We prove a formula for the Fourier coefficients of the Siegel Eisenstein series of degree n, weight k and character χ under certain conditions on χ. We also prove the existence of Λ-adic Siegel Eisenstein series of degree n.