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Mock modular forms and geometric theta functions for indefinite quadratic forms

Funke, Jens; Kudla, Stephen S.

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Authors

Stephen S. Kudla



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 Mar 29, 2024
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

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Accepted Journal Article (290 Kb)
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Publisher Licence URL
http://creativecommons.org/licenses/by-nc-nd/4.0/

Copyright Statement
This is an author-created, un-copyedited version of an article published in Journal of Physics A: Mathematical and Theoretical. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1751-8121/aa848b As the Version of Record of this article has been published on a subscription basis, this Accepted Manuscript is available for reuse under a CC BY-NC-ND 3.0 licence after a 12 month embargo period.




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