Restricting Hecke-Siegel operators to Jacobi modular forms |
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Authors: | Lynne H. Walling |
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Affiliation: | Department of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom |
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Abstract: | We compute the action of Hecke operators on Jacobi forms of “Siegel degree” n and m×m index M, provided 1?j?n−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), Tj(p2) (n−m<j?n) 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 detM|detM′. 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. |
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Keywords: | 11F41 |
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