Extending a Catalog of Mock and Quantum Modular Forms to an Infinite Class

Authors

Allison Arnold-Roksandich, Boise State UniversityFollow
Brian Diaz
Erin Ellefsen
Holly Swisher, Oregon State University

Document Type

Article

Publication Date

6-2020

Abstract

Utilizing a classification due to Lemke Oliver of eta-quotients which are also theta functions (here called eta-theta functions), Folsom, Garthwaite, Kang, Treneer, and the fourth author constructed a catalog of mock modular forms V_mn having weight 3/2 eta-theta function shadows and showed that these mock modular forms when viewed on certain sets of rationals, transform as quantum modular forms under the action of explicit subgroups. In this paper, we introduce an infinite class of functions that generalizes one row of the catalog, namely the V_m1, and show that the functions in this infinite class are both mock modular and quantum modular forms.

Publication Information

Arnold-Roksandich, Allison; Diaz, Brian; Ellefsen, Erin; and Swisher, Holly. (2020). "Extending a Catalog of Mock and Quantum Modular Forms to an Infinite Class". Research in Number Theory, 6(2), . https://doi.org/10.1007/s40993-020-00192-3