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Journal of Lie Theory 11 (2001), No. 2, 545--557
Copyright Heldermann Verlag 2001

Jacobi Forms on Symmetric Domains and Torus Bundles over Abelian Schemes

Min Ho Lee
Dept. of Mathematics, University of Northern Iowa, Cedar Falls, IA 50614, U.S.A.

We introduce Jacobi forms on Hermitian symmetric domains using automorphy factors associated to torus bundles over abelian schemes. We discuss families of modular forms determined by such Jacobi forms and prove that these Jacobi forms reduce to the usual Jacobi forms of several variables when the Hermitian symmetric domain is a Siegel upper half space.

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