Functional Equation for Theta Series
Jae-Hyun Yang
TL;DR
This paper derives a transformation formula for theta series under the Jacobi modular group, extending Mumford's earlier results to a broader context in the Siegel-Jacobi space.
Contribution
It provides a generalized transformation formula for theta series under the Jacobi modular group, expanding upon Mumford's classical formula.
Findings
Derived a new transformation formula for theta series
Extended Mumford's formula to the Siegel-Jacobi space
Enhanced understanding of theta series behavior under modular transformations
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].
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic structures and combinatorial models · Advanced Topics in Algebra