Theta Series Associated with the Weil-Schroedinger Representation

2007/09/01 by Jae-Hyun Yang, Yang, Jae-Hyun
Mathematics · #11F27 #11F50 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT #msc:11F27 #msc:11F50

paper · pdf · doi:10.48550/arxiv.0709.0071

18 pages : correction of several minor errors : added Theorem 6.2

arxiv created 2009/08/03 · arxiv updated 2009/12/01

Abstract

The Weil representation discovered by Andre Weil plays an important role in the study of the tranformation properties of theta series. In this paper, we define the Weil-Schroedinger representation of the Jacobi group and prove that the theta series associated with the Weil-Schroedinger representation is a Jacobi form with respect to a suitable arithmetic subgroup of the Jacobi modular group.

Related

• The Weil Representations of the Jacobi Group
• Functional Equation for Theta Series
• Heisenberg Groups, Theta Functions and the Weil Representation
• Jacobi Forms of Critical Weight and Weil Representations
• The Schroedinger-Weil Representation and Jacobi Forms of Half-Integral Weight