Mock modular forms and geometric theta functions for indefinite quadratic forms

Funke, Jens; Kudla, Stephen S.

Abstract

Theta functions for indefinite quadratic forms are an important tool to construct modular forms and Mock modular forms. In this note, we recall the representation-theoretic background in the construction of theta series with emphasis on the theory developed by the second-named author with Millson. We then employ this machinery to define a theta integral for any signature, for which we provide a natural splitting into a holomorphic part with geometric meaning and its non-holomorphic modular completion. In particular, specializing to hyperbolic space, we recover Zweger's Mock theta function from a geometric perspective.

Citation

Funke, J., & Kudla, S. S. (2017). Mock modular forms and geometric theta functions for indefinite quadratic forms. Journal of Physics A: Mathematical and Theoretical, 50(40), Article 404001. https://doi.org/10.1088/1751-8121/aa848b

• Journal Article Type: Article
• Acceptance Date: Aug 7, 2017
• Online Publication Date: Sep 5, 2017
• Publication Date: Oct 6, 2017
• Deposit Date: Apr 28, 2017
• Publicly Available Date: Sep 5, 2018
• Journal: Journal of Physics A: Mathematical and Theoretical
• Print ISSN: 1751-8113
• Electronic ISSN: 1751-8121
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 50
• Issue: 40
• Article Number: 404001
• DOI: https://doi.org/10.1088/1751-8121/aa848b
• Public URL: https://durham-repository.worktribe.com/output/1359828