Differential operators for Hermitian Jacobi forms and Hermitian modular forms

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• 作者：James D. Martin ; Jayantha Senadheera
• 关键词：Hermitian Jacobi forms ; Hermitian modular forms ; Rankin–Cohen brackets
• 刊名：The Ramanujan Journal
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：42
• 期：2
• 页码：443-451
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Number Theory; Field Theory and Polynomials; Combinatorics; Fourier Analysis; Functions of a Complex Variable;
• 出版者：Springer US
• ISSN：1572-9303
• 卷排序：42

文摘

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).