Document Type
Article
Publication Date
2016
Keywords
Theta functions, Mock modular forms, Quantum modular forms
Abstract
In 2013, Lemke Oliver classified all eta-quotients which are theta functions. In this paper, we unify the eta–theta functions by constructing mock modular forms from the eta–theta functions with even characters, such that the shadows of these mock modular forms are given by the eta–theta functions with odd characters. In addition, we prove that our mock modular forms are quantum modular forms. As corollaries, we establish simple finite hypergeometric expressions which may be used to evaluate Eichler integrals of the odd eta–theta functions, as well as some curious algebraic identities.
Publication Title
Research in Number Theory
Volume
2
Issue
1
First Page
14
DOI
10.1007/s40993-016-0045-7
Required Publisher's Statement
© 2016 The Author(s)
Recommended Citation
Folsom, A., Garthwaite, S., Kang, SY. et al. Res. Number Theory (2016) 2: 14. https://doi.org/10.1007/s40993-016-0045-7
Subjects - Topical (LCSH)
Functions, Theta; Forms, Modular
Genre/Form
articles
Type
Text
Rights
Copying of this document in whole or in part is allowable only for scholarly purposes. It is understood, however, that any copying or publication of this document for commercial purposes, or for financial gain, shall not be allowed without the author’s written permission.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Language
English
Format
application/pdf
