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

Hirakjyoti Das; Manjil P. Saikia; Abhishek Sarma

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arXiv · 2409.02929

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

Hirakjyoti Das·Manjil P. Saikia·Abhishek Sarma

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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.

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Hirakjyoti Das, Manjil P. Saikia, Abhishek Sarma. 2024-08-20. Arithmetic Properties modulo powers of $2$ and $3$ for Overpartition $k$-Tuples with Odd Parts. https://arxiv.org/abs/2409.02929

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