The Schroedinger-Weil Representation and Jacobi Forms of Half-Integral Weight

Details The Schroedinger-Weil Representation and Jacobi Forms of Half-Integral Weight The Schroedinger-Weil Representation and Jacobi Forms of Half-Integral Weight

2009-08-03

arxiv.org/abs/0908.0252v2

Mathematics

Number Theory

25 pages ; correction of many typos ; change of some notations

Scientific paper

In this paper, we define the concept of Jacobi forms of half-integral weight using Takase's automorohic factor of weight 1/2 for a two-fold covering group of the symplectic group on the Siegel upper half plane and find covariant maps for the Schroedinger-Weil representation. Using these covariant maps, we construct Jacobi forms of half-integral weight with respect to an arithmetic subgroup of the Jacobi group.

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