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A trace formula for Jacobi forms. (English) Zbl 0651.10019
The authors state and derive a completely explicit trace formula for double coset operators acting on spaces of Jacobi forms. As a side result some nice formulas concerning Gauss sums drop out. A specialization of this general trace formula is considered in the paper reviewed below [Invent. Math. 94, No. 1, 113–146 (1988; Zbl 0651.10020)]. Here it turns out that the space of Jacobi forms of weight $$k$$ and index $$m$$ is Hecke equivariantly isomorphic to a certain subspace of elliptic modular forms of weight $$2k-2$$ and level $$m$$.
Reviewer: N.-P. Skoruppa

MSC:
 11F50 Jacobi forms 11F72 Spectral theory; trace formulas (e.g., that of Selberg) 11L03 Trigonometric and exponential sums, general
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