Automorphic properties of generating functions for generalized odd rank moments and odd Durfee symbols

Abstract

We define two-parameter generalizations of Andrews' $(k+1)$-marked odd Durfee symbols and $2k$th symmetrized odd rank moments, and study the automorphic properties of some of their generating functions. When $k=0$ we obtain families of modular forms and mock modular forms. When $k\ge 1$, we find quasimodular forms and quasimock modular forms.

References in corpus (4)

• Mock Theta Functions
• Rank and crank moments for overpartitions
• Transformation Formula of the "2nd" Order Mock Theta Function
• Automorphic properties of generating functions for generalized rank moments and Durfee symbols

Cited by in corpus (6)

• The Bailey chain and mock theta functions
• Renormalization and quantum modular forms, part II: Mock theta functions
• Mixed mock modular q-series
• An analogue of $k$-marked Durfee symbols for strongly unimodal sequences
• Bailey Pairs and an Identity of Chern-Li-Stanton-Xue-Yee
• Generating Functions of the Hurwitz Class Numbers Associated with Certain Mock Theta Functions