The mixed mock modularity of certain duals of generalized quantum modular forms of Hikami and Lovejoy

TL;DR

This paper expresses a family of sums related to duals of generalized quantum modular forms as mixed mock modular forms, using Appell and theta functions, advancing understanding of their modular properties.

Contribution

It introduces a new representation of Hikami and Lovejoy's sums as mixed mock modular forms, linking them to Appell and theta functions for the first time.

Findings

Expressed sums in terms of Appell functions

Connected sums to theta functions

Enhanced understanding of modular properties

Abstract

We express a family of Hecke--Appell-type sums of Hikami and Lovejoy in terms of mixed mock modular forms; in particular, we express the sums in terms of Appell functions and theta functions. Hikami and Lovejoy's family of Hecke--Appell-type sums was obtained by considering certain duals of generalized quantum modular forms.