Ikeda\u27s conjecture on the period of the Duke-Imamoglu-Ikeda lift

Let k and n be positive even integers. For a cuspidal Hecke eigenform h in the Kohnen plus space of weight k - n/2 + 1/2 for Γ0(4), let In(h) be the Duke-Imamoglu-Ikeda lift of h in the space of cusp forms of weight k for Spn(Z), and f the primitive form of weight 2k - n for SL2(Z) corresponding to h under the Shimura correspondence. We then express the ratio / of the period of In(h) to that of h in terms of special values of certain L-functions of f. This proves the conjecture proposed by Ikeda concerning the period of the Duke-Imamoglu-Ikeda lift