IKEDA'S CONJECTURE ON THE PERIOD OF THE DUKE-IMAMOGLU-IKEDA LIFT

Let k and n be positive even integers. For a primitive form f in S2k−n(SL2(Z)), let In(f) be the Duke-Imamo¯glu-Ikeda lift of f to Sk(Spn(Z)), and e f the cusp form in Kohnen’s plus subspace of weight k¡n/2+1/2 for Γ0(4) corresponding to f under the Shimura correspondence. We then express the ratio hIn(f), In(f)i h e f, e fi of the period of In(f) to that of e f in terms of special values of certain L-functions of f. This proves the conjecture proposed by Ikeda [Ike06] concerning the period of the Duke-Imamo¯glu-Ikeda lift