Arithmetic Properties of Generalized Cubic and Overcubic Partitions
Number Theory
2026-04-29 v2
Abstract
We prove several congruences satisfied by the generalized cubic and generalized overcubic partition functions, recently introduced by Amdeberhan, Sellers, and Singh. We also prove infinite families of congruences modulo powers of and modulo satisfied by the generalized overcubic partitions, as well as some density results that they satisfy. We use both elementary -series techniques as well as the theory of modular forms to prove our results.
Cite
@article{arxiv.2503.19399,
title = {Arithmetic Properties of Generalized Cubic and Overcubic Partitions},
author = {Hirakjyoti Das and Saikat Maity and Manjil P. Saikia},
journal= {arXiv preprint arXiv:2503.19399},
year = {2026}
}
Comments
18 pages, some results removed