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Koecher-Maass series of a certain half-integral weight modular form related to the Duke-Imamoḡlu-Ikeda lift

Hidenori KatsuradaHisa-aki Kawamura — 2014

Acta Arithmetica

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 f be the corresponding primitive form of weight 2k-n for SL₂(ℤ) under the Shimura correspondence, and Iₙ(h) the Duke-Imamoḡlu-Ikeda lift of h to the space of cusp forms of weight k for Spₙ(ℤ). Moreover, let ϕ I ( h ) , 1 be the first Fourier-Jacobi coefficient of Iₙ(h), and σ n - 1 ( ϕ I ( h ) , 1 ) be the cusp form in the generalized Kohnen plus space of weight k - 1/2 corresponding to ϕ I ( h ) , 1 under the...

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