Universität zu Köln

Bringmann, Kathrin, Kaszian, Jonas, Milas, Antun and Nazaroglu, Caner ORCID: 0000-0001-8844-2441 (2021). Integral representations of rank two false theta functions and their modularity properties. Res. Math. Sci., 8 (4). CHAM: SPRINGER INT PUBL AG. ISSN 2197-9847

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Abstract

False theta functions form a family of functions with intriguing modular properties and connections to mock modular forms. In this paper, we take the first step towards investigating modular transformations of higher rank false theta functions, following the example of higher depth mock modular forms. In particular, we prove that under quite general conditions, a rank two false theta function is determined in terms of iterated, holomorphic, Eichler-type integrals. This provides a new method for examining their modular properties and we apply it in a variety of situations where rank two false theta functions arise. We first consider generic parafermion characters of vertex algebras of type A(2) and B-2. This requires a fairly non-trivial analysis of Fourier coefficients of meromorphic Jacobi forms of negative index, which is of independent interest. Then we discuss modularity of rank two false theta functions coming from superconformal Schur indices. Lastly, we analyze Z -invariants of Gukov, Pei, Putrov, and Vafa for certain plumbing H-graphs. Along the way, our method clarifies previous results on depth two quantum modularity.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Bringmann, Kathrin UNSPECIFIED UNSPECIFIED UNSPECIFIED Kaszian, Jonas UNSPECIFIED UNSPECIFIED UNSPECIFIED Milas, Antun UNSPECIFIED UNSPECIFIED UNSPECIFIED Nazaroglu, Caner UNSPECIFIED orcid.org/0000-0001-8844-2441 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-584322
DOI:	10.1007/s40687-021-00284-1
Journal or Publication Title:	Res. Math. Sci.
Volume:	8
Number:	4
Date:	2021
Publisher:	SPRINGER INT PUBL AG
Place of Publication:	CHAM
ISSN:	2197-9847
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language MAASS FORMS; ALGEBRAS; SERIES Multiple languages Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/58432