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The Ramanujan Journal

, Volume 42, Issue 2, pp 443–451 | Cite as

Differential operators for Hermitian Jacobi forms and Hermitian modular forms

  • James D. Martin
  • Jayantha Senadheera
Article
  • 180 Downloads

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).

Keywords

Hermitian Jacobi forms Hermitian modular forms Rankin–Cohen brackets 

Mathematics Subject Classification

Primary 11F55 Secondary 11F60 

Notes

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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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of North TexasDentonUSA
  2. 2.Department of Mathematics and Computer Science, Faculty of Natural SciencesThe Open University of Sri LankaNawalaSri Lanka

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