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)

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

Creative Commons Attribution 4.0 License
This work is licensed under a Creative Commons Attribution 4.0 License.

Language

English

Format

application/pdf

Included in

Mathematics Commons

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