Local Weak Maass Forms and Traces of Cycle Integrals

Using relations established by Bringmann and Kane in a recent preprint based on the function ${\omega }_{k+1,D}$ studied by Mono, Rolen, and the second author, we introduce two further functions naturally associated with a construction by Bringmann and Mono. We exploit results by Löbrich–Schwagenscheidt, Mono, and the second author on representations of these functions as traces of cycles integrals in order to provide more identities of the same kind.