arXiv subjects

HemanthKumar B

Publications and source records attributed to HemanthKumar B.

2 recordsLinked to original sources

arXiv2025

On 2-color partitions where one of the colors is multiples of $7^k$

In this work, we investigate the arithmetic properties of $p_{1,7^k}(n)$, which counts 2-color partitions of $n$ where one of the colors appears only in parts that are multiples of $7^k$. By constructing generating functions for $p_{1,7^k}(n)$ across specific arithmetic progressions, we establish a set of Ramanujan-type infinite family of congruences modulo powers of $7$.

math.NT↗

arXiv2025

On $7^k$-regular partitions modulo powers of $7$

In this study, we explore the arithmetic properties of $b_{7^k}(n)$ for any $k\geq1$, which enumerates the partitions of $n$ where no part is divisible by $7^k$. By constructing generating functions for $b_{7^k}(n)$ over specific arithmetic progressions, we establish a collection of Ramanujan-type congruences.

math.NT↗