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Differential operators for Hermitian Jacobi forms and Hermitian modular forms

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Abstract

Kim (Arch Math (Basel) 79(3):208–215, 2002) constructs multilinear differential operators for Hermitian Jacobi forms and Hermitian modular forms. However, her work relies on incorrect actions of differential operators on spaces of Hermitian Jacobi forms and Hermitian modular forms. In particular, her results are incorrect if the underlying field is the Gaussian number field. We consider more general spaces of Hermitian Jacobi forms and Hermitian modular forms over \(\mathbb {Q}(i)\), which allow us to correct the corresponding results in Kim (2002).

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Acknowledgments

We thank Olav Richter for his help and guidance in writing this paper. We also thank the anonymous referee for many helpful comments.

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Correspondence to James D. Martin.

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Martin, J.D., Senadheera, J. Differential operators for Hermitian Jacobi forms and Hermitian modular forms. Ramanujan J 42, 443–451 (2017). https://doi.org/10.1007/s11139-015-9761-1

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  • DOI: https://doi.org/10.1007/s11139-015-9761-1

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