KOECHER-MAASS SERIES OF THE IKEDA LIFT FOR U(m,m)

Let K = Q( √ −D) be an imaginary quadratic field with discriminant −D, and χ the Dirichlet character corresponding to the extension K/Q. Let m = 2n or 2n + 1 with n a positive integer. Let f be a primitive form of weight 2k + 1 and character χ for Γ0(D), or a primitive form of weight 2k for SL2(Z) according as m = 2n, or m = 2n + 1. For such an f let Im(f) be the lift of f to the space of Hermitian modular forms constructed by Ikeda. We then give an explicit formula of the Koecher-Maass series L(s, Im(f)) of Im(f). This is a generalization of Mizuno [Mi0