Functional Equation for Theta Series
Number Theory
2008-09-06 v5
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].
Keywords
Cite
@article{arxiv.0707.3276,
title = {Functional Equation for Theta Series},
author = {Jae-Hyun Yang},
journal= {arXiv preprint arXiv:0707.3276},
year = {2008}
}
Comments
Added the detailed proof ; added 4 more references ; Removal of Remark 2.3