Osaka Journal of Mathematics

A generalization of vector valued Jacobi forms

Tomoyoshi Ibukiyama and Ryoji Kyomura

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Abstract

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

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

Dates
First available in Project Euclid: 26 September 2011

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1317044947

Mathematical Reviews number (MathSciNet)
MR2837681

Zentralblatt MATH identifier
1246.11103

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

Citation

Ibukiyama, Tomoyoshi; Kyomura, Ryoji. A generalization of vector valued Jacobi forms. Osaka J. Math. 48 (2011), no. 3, 783--808. https://projecteuclid.org/euclid.ojm/1317044947


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References

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