Restricted Overpartitions and concave compositions: their modularity and asymptotics
Number Theory
2026-04-06 v2 Combinatorics
Abstract
In this paper we study restricted overpartitions and concave compositions. In several cases the resulting generating functions involve simultaneously modular forms, mock theta functions, mock Maass theta functions, and false theta functions, illustrating the appearance of mixed modular structures in restricted partition problems. Moreover, we obtain their asymptotic main terms. We also study related rank statistics.
Cite
@article{arxiv.2601.03998,
title = {Restricted Overpartitions and concave compositions: their modularity and asymptotics},
author = {Koustav Banerjee and Kathrin Bringmann and Atul Dixit},
journal= {arXiv preprint arXiv:2601.03998},
year = {2026}
}