Arithmetic properties modulo powers of $2$ for overpartition $k$-tuples with odd parts
Number Theory
2024-08-23 v2
Abstract
Recently, Drema and Saikia (2023) proved several congruences modulo powers of 2 and 3 for overpartition triples with odd parts. We extend their list substantially. We prove several congruences modulo powers of 2 for overpartition k-tuples with odd parts, along with a few infinite families of congruences for overpartition triples with odd parts and for overpartition k-tuples with odd parts (for k = 4 and for odd k).
Keywords
Cite
@article{arxiv.2312.12011,
title = {Arithmetic properties modulo powers of $2$ for overpartition $k$-tuples with odd parts},
author = {Manjil P. Saikia and Abhishek Sarma and James A. Sellers},
journal= {arXiv preprint arXiv:2312.12011},
year = {2024}
}
Comments
25 pages, final version, typos and minor errors fixed after referee report, Theorem 2.3 strengthened, to appear in the Journal of the Ramanujan Mathematical Society