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On the Fourier–Jacobi expansion of the unitary Kudla lift

Published online by Cambridge University Press:  19 January 2007

Atsushi Murase  and
Takashi Sugano
Atsushi Murase
Affiliation:
Department of Mathematical Science, Faculty of Science, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-ku, Kyoto 603-8555, Japanmurase@cc.kyoto-su.ac.jp
Takashi Sugano
Affiliation:
Department of Mathematics, Faculty of Science, Kanazawa University, Kakuma-machi, Kanazawa 920-1192, Japansugano@kappa.s.kanazawa-u.ac.jp
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Abstract

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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 $\mathcal{L} f$.

Keywords

automorphic formsFourier–Jacobi expansiontheta liftKudla liftunitary groups11F55 (primary)11F6711F70 (secondary)
Type
Research Article
Information
Compositio Mathematica , Volume 143 , Issue 1 , January 2007 , pp. 1 - 46
Copyright
Foundation Compositio Mathematica 2007