Let k and n be positive even integers. For a cuspidal Hecke eigenformh in the Kohnen plus space of weight k - n/2 + 1/2 for Γ0(4); let f bethe corresponding primitive form of weight 2k - n for SL2(Z) under the Shimura correspondence, and In(h) the Duke-Imamoglu-Ikeda lift of h tothe space of cusp forms of weight k for Spn(Z). Moreover, let φIn(h),1 be the rst Fourier-Jacobi coe cient of In(h), and σn-1(φIn(h),1) be the cusp form in the generalized Kohnen plus space of weight k - 1/2 corresponding toφIn(h),1 under the Ibukiyama isomorphism. We give an explicit formula for the Koecher-Maass series L(s, σn-1( In(h),1)) of n-1(φIn(h);1) expressed interms of the usual L-functions of h and f.
Koecher-Maass series of a certain half-integral weight modular form related to the Duke-Imamaglu-Ikeda lift
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