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Journal Article

A trace formula for Jacobi forms.


Zagier,  Don
Max Planck Institute for Mathematics, Max Planck Society;

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Skoruppa, N.-P., & Zagier, D. (1989). A trace formula for Jacobi forms. Journal für die Reine und Angewandte Mathematik, 393, 168-198.

Cite as: http://hdl.handle.net/21.11116/0000-0004-393F-7
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 (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.