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2 results

  • On the Fourier–Jacobi expansion of the unitary Kudla lift

  • Atsushi Murase, Takashi Sugano
  • Journal:
    Compositio Mathematica / Volume 143 / Issue 1 / January 2007
    Published online by Cambridge University Press:
    19 January 2007, pp. 1-46
    Print publication:
    January 2007
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  • We study a theta lift from a cusp form $f$ on $U(1,1)$ to a cusp form $\mathcal{L} f$ on $U(2,1)$ (the unitary Kudla lift of $f$). We give an explicit expression of the Fourier–Jacobi expansion of $\mathcal{L} f$ in terms of periods and Hecke eigenvalues of $f$. As an application, we give a criterion for the nonvanishing of $\mathcal{L} f$.

  • Fourier–Jacobi Type Spherical Functions for Discrete Series Representations of Sp(2, $\Bbb R$)

  • Miki Hirano
  • Journal:
    Compositio Mathematica / Volume 128 / Issue 2 / September 2001
    Published online by Cambridge University Press:
    04 December 2007, pp. 177-216
    Print publication:
    September 2001
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  • In this paper we define a kind of generalized spherical functions on Sp(2, $\Bbb R$). We call it ‘Fourier–Jacobi type’, since it can be considered as a generalized Whittaker model associated with the Jacobi maximal parabolic subgroup. Also we give the multiplicity theorem and an explicit formula of these functions for discrete series representations of Sp(2, $\Bbb R$).