Abstract:
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In 1985 Eichler and Zagier defined the Jacobi form as a common generalization of theta functions, modular forms, and elliptic functions. Given an even positive-definitte lattice, the associated Jacobi forms form a graded ring. It is an open problem whether this ring is finitely generated. In this talk we will first briefly introduce the theory of Jacobi forms, and then discuss the ring structure of Jacobi forms associated with irreducible root systems, rank-two lattices and the Leech lattice.
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