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Jacobi Forms of Several Variables and the Maaß Space

✍ Scribed by Aloys Krieg

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
661 KB
Volume
56
Category
Article
ISSN
0022-314X

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✦ Synopsis

In this paper we describe the space of Jacobi forms on H_C n . This type of Jacobi forms appears in the Fourier Jacobi expansions of all kinds of modular forms of several variables. We can characterize the space of Jacobi forms of weight k by vector valued elliptic modular forms of weight k&nÂ2. Then we use the Jordan theoretic language in order to describe modular forms on the orthogonal group O(2, n+2), whose Fourier Jacobi expansions also yield Jacobi forms of our type. Finally we determine a Maa? space as the isomorphic image of a particular space of Jacobi forms. Especially our procedure guarantees the existence of certain nontrivial singular modular forms.

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