Banerjee, KoustavKoustavBanerjeeBringmann, KathrinKathrinBringmannDixit, AtulAtulDixit2026-01-142026-01-142026-01-012331-842210.48550/arXiv.2601.03998https://repository.iitgn.ac.in/handle/IITG2025/33932In this paper we study restricted overpartitions and concave compositions. Using q-series transformations, we show that their generating functions are related to modular forms, mock theta functions, false theta functions, and mock Maass theta functions. Moreover, we obtain their asymptotic main terms. We also study related rank statistics.en-USAsymptoticsConcave compositionsFalse theta functionsMock theta functionsMock Maass theta functionsModular formsOverpartitionsTauberian theoreme-Print