title: On the modularity of certain functions from the Gromov-Witten theory of elliptic orbifolds.
abstract: In this paper, we study modularity of several functions which naturally arose in a recent paper of Lau and Zhou on open Gromov-Witten potentials of elliptic orbifolds. They derived a number of examples of indefinite theta functions, and we provide modular completions for several such functions which involve more complicated objects than ordinary modular forms. In particular, we give new closed formulae for special indefinite theta functions of type (1,2) in terms of products of mock modular forms. This formula is also of independent interest.
authors.affiliation: Mathematical Institute, University of Cologne , Weyertal 86-90, 50931 Cologne, Germany.
authors.forename: Kathrin
authors.initials: K
authors.lastname: Bringmann
authors.affiliation: Mathematical Institute, University of Cologne , Weyertal 86-90, 50931 Cologne, Germany.
authors.forename: Larry
authors.initials: L
authors.lastname: Rolen
authors.affiliation: Mathematical Institute, University of Cologne , Weyertal 86-90, 50931 Cologne, Germany.
authors.forename: Sander
authors.initials: S
authors.lastname: Zwegers
keywords: Gromov–Witten potentials; Jacobi forms; elliptic orbifolds; mock modular forms; modular forms