On the period of the Ikeda lift for U(m,m)

Let K be an imaginary quadratic field, and x 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 and nebentype x, or a primitive form of weight 2k for SL(2,Z) according as m=2n, or m=2n+1. For such an f let I_m(f) be the lift of f to the space of modular forms of weight 2k+2n for the Hermitian modular group of degree m constructed by Ikeda. We then express the period <I_m(f), I_m(f) > of I_m(f) in terms of special values of the adjoint L-functions of f. This poves the conjecture concerning the period of the Ikeda lift proposed by Ikeda.