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Internal congruences modulo powers of 2 for $k$-colored overpartitions into odd parts
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- OpenAlex
- Published in
- arXiv (Cornell University)
- DOI
- 10.48550/arxiv.2609.11806
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Abstract
Let $\overline{po}_k(n)$ denote the number of $k$-colored overpartitions of $n$ into odd parts. For every odd number of colors, we establish infinite families of internal congruences modulo high powers of $2$. The proof proceeds by expressing the relevant difference generating functions as a fixed theta quotient multiplied by polynomials in an auxiliary function. Uniform lower bounds for the $2$-adic valuations of the polynomial coefficients then yield the stated internal congruences. These results generalize an internal congruence of Saikia, Sarma and Sellers (J. Ramanujan Math. Soc.~2025) on overpartition triples into odd parts.
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