Quantum Mock Modular Forms Arising From Eta-Theta Functions

Authors

Amanda Folsom, Amherst CollegeFollow
Sharon Garthwaite, Bucknell UniversityFollow
Soon-Yi Kang, Kangwon National UniversityFollow
Holly Swisher, Oregon State UniversityFollow
Stephanie Treneer, Western Washington UniversityFollow

Publication Date

8-8-2016

Description

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.

Journal

Research in Number Theory

Volume

2

Department

Mathematics

Link to Published Version

http://resnumtheor.springeropen.com/articles/10.1007/s40993-016-0045-7

Recommended Citation

Folsom, Amanda; Garthwaite, Sharon; Kang, Soon-Yi; Swisher, Holly; Treneer, Stephanie, Quantum mock modular forms arising from eta-theta functions. Res. Number Theory 2 (2016), Art. 14, 41 pp.