Functional Equation for Theta Series
arXiv:0707.3276
Abstract
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].
Added the detailed proof ; added 4 more references ; Removal of Remark 2.3