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Mock modular forms and geometric theta functions for indefinite quadratic forms.

Funke, Jens and Kudla, Stephen S. (2017) 'Mock modular forms and geometric theta functions for indefinite quadratic forms.', Journal of physics A : mathematical and theoretical., 50 (40). p. 404001.


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.

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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Publisher 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 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.
Date accepted:07 August 2017
Date deposited:14 August 2017
Date of first online publication:05 September 2017
Date first made open access:05 September 2018

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