On the modularity of certain functions from the Gromov-Witten theory of\n elliptic orbifolds

In this paper, we study modularity of several functions which naturally arose\nin a recent paper of Lau and Zhou on open Gromov-Witten potentials of elliptic\norbifolds. They derived a number of examples of indefinite theta functions, and\nwe provide modular completions for several such functions which involve more\ncomplicated objects than ordinary modular forms. In particular, we give new\nclosed formulas for special indefinite theta functions of type $(1,2)$ in terms\nof products of mock modular forms. This formula is also of independent\ninterest.\n