Osaka Journal of Mathematics

A generalization of vector valued Jacobi forms

Tomoyoshi Ibukiyama and Ryoji Kyomura

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The Fourier--Jacobi coefficients of vector valued Siegel modular forms of degree $n$ are more general functions than vector valued Jacobi forms defined by Ziegler [9] even when $n=2$. We define generalized vector valued Jacobi forms corresponding to the above coefficients when $n=2$ and prove that such a space is isomorphic to a certain product of spaces of usual scalar valued Jacobi forms of various weights. This isomorphism is realized by certain linear holomorphic differential operators. The half-integral weight case is also treated.

Article information

Osaka J. Math., Volume 48, Number 3 (2011), 783-808.

First available in Project Euclid: 26 September 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11F50: Jacobi forms 11F46: Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms


Ibukiyama, Tomoyoshi; Kyomura, Ryoji. A generalization of vector valued Jacobi forms. Osaka J. Math. 48 (2011), no. 3, 783--808.

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