Arithmetic Properties modulo powers of $2$ and $3$ for Overpartition $k$-Tuples with Odd Parts

Hirakjyoti Das; Manjil P. Saikia; Abhishek Sarma

Arithmetic Properties modulo powers of $2$ and $3$ for Overpartition $k$-Tuples with Odd Parts

Number Theory 2026-04-29 v2

Authors: Hirakjyoti Das , Manjil P. Saikia , Abhishek Sarma

Abstract

Recently, Drema and N. Saikia (2023) and M. P. Saikia, Sarma, and Sellers (2023) proved several congruences modulo powers of $2$ for overpartition triples with odd parts. In this paper, we study further divisibility properties of overpartition $k$ -tuples with odd parts using elementary means as well as properties of modular forms. In particular, we prove several congruences modulo multiples of $3$ , and an infinite family of congruences modulo powers of $3$ ; we also prove some cases of a conjecture of Saikia, Sarma, and Sellers.

Keywords

overpartition k-tuples odd parts congruences modular forms divisibility properties powers of 2 and 3

Cite

@article{arxiv.2409.02929,
  title  = {Arithmetic Properties modulo powers of $2$ and $3$ for Overpartition $k$-Tuples with Odd Parts},
  author = {Hirakjyoti Das and Manjil P. Saikia and Abhishek Sarma},
  journal= {arXiv preprint arXiv:2409.02929},
  year   = {2026}
}

Comments

22 pages, final version, accepted at the Bulletin of the Malaysian Mathematical Sciences Society

Arithmetic Properties modulo powers of $2$ and $3$ for Overpartition $k$-Tuples with Odd Parts

Abstract

Keywords

Cite

Comments

Related papers