English

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 22 and modulo 1212 satisfied by the generalized overcubic partitions, as well as some density results that they satisfy. We use both elementary qq-series techniques as well as the theory of modular forms to prove our results.

Keywords

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

R2 v1 2026-06-28T22:33:26.370Z