Restricting Hecke–Siegel operators to Jacobi modular forms

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• 作者：Lynne H. Walling
• 关键词：Jacobi modular forms ; Siegel modular forms ; Hecke operators ; Lifts
• 刊名：Journal of Number Theory
• 出版年：2009
• 出版时间：July 2009
• 年：2009
• 卷：129
• 期：7
• 页码：1709-1733
• 全文大小：309 K

文摘

We compute the action of Hecke operators on Jacobi forms of “Siegel degree” n and m×m index M, provided 1jn−m. We find they are restrictions of Hecke operators on Siegel modular forms, and we compute their action on Fourier coefficients. Then we restrict the Hecke–Siegel operators T(p), T_j(p²) (n−m<jn) to Jacobi forms of Siegel degree n, compute their action on Fourier coefficients and on indices, and produce lifts from Jacobi forms of index M to Jacobi forms of index M^′ where detMdetM^′. Finally, we present an explicit choice of matrices for the action of the Hecke operators on Siegel modular forms, and for their restrictions to Jacobi modular forms.