Jae-Hyun Yang
Published 2007-07-22, updated 2008-09-06Version 5
In this short paper, we find the transformation formula for the theta series under the action of the Jacobi modular group on the Siegel-Jacobi space. This formula generalizes the formula (5.1) obtained by Mumford in his book[p.189, Tata Lectures on Theta I (1983), Birkhauser].
Comments: Added the detailed proof ; added 4 more references ; Removal of Remark 2.3
Theta Series Associated with the Weil-Schroedinger Representation
Cubic identities for theta series in three variables
Reduction mod $\ell$ of Theta Series of Level $\ell^n$
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