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B. Hemanthkumar

Publications and source records attributed to B. Hemanthkumar.

6 recordsLinked to original sources
arXiv2026

On an Overpartition Analogue of $SOME(n)$

Recently, Andrews and Dastidar introduced the partition function $SOME(n)$, defined as the sum of all the odd parts in the partitions of $n$ minus the sum of all the even parts in the partitions of $n$. They derived its generating function and established some congruences satisfied by \(SOME(n)\). In this paper, we introduce an overpartition analogue of $SOME(n)$, denoted by $\overline{SOME}(n)$, the sum of all the odd parts in the overpartitions of \(n\) minus the sum of all the even parts in the overpartitions of \(n\). We derive the generating function for $\overline{SOME}(n)$ and obtain congruences modulo \(3, \ 5\) and powers of \(2\). Our method is based on classical $q$-series identities and manipulations of infinite products and sums.

math.CO↗
arXiv2025

On $\ell-$regular and $2-$color partition triples modulo powers of $3$

Let $T_\ell(n)$ denote the number of $\ell-$regular partition triples of $n$ and let $p_{\ell, 3}(n)$ enumerates the number of 2--color partition triples of $n$ where one of the colors appear only in parts that are multiples of $\ell$. In this paper, we prove several infinite families of congruences modulo powers of 3 for $T_\ell(n)$ and $p_{\ell, 3}(n)$, where $\ell \geq 1$ and $\equiv 0\pmod{3^k}$, and $\equiv \pm 3^k \pmod{3^{k+1}}$.

math.CO↗
arXiv2020

$P$--$Q$ "mixed" modular equations of degree 15

Ramanujan in his second notebook recorded total of seven $P$--$Q$ modular equations involving theta--function $f(-q)$ with moduli of orders 1, 3, 5 and 15. In this paper, modular equations analogous to those recorded by Ramanujan are obtained involving his theta--functions $\varphi(q)$ and $\psi(-q)$ with moduli of orders 1, 3, 5 and 15. As a consequence, several values of quotients of theta--function and a continued fraction of order 12 are explicitly evaluated.

math.NT↗
arXiv2019

Congruence properties of coefficients of the eighth order mock theta function $V_0(q)$

We study the divisibility properties of the partition function associated with the eighth order mock theta function $V_0(q)$, introduced by Gordon and McIntosh. We obtain congruences modulo powers of 2 for certain coefficients of the partition function, akin to Ramanujan's partition congruences. Further, we also present several infinite families of congruences molulo 13, 25 and 27.

math.NT↗
arXiv2019

On eight colour partitions

In this article, we study the arithmetic properties of the partition function $p_8(n)$, the number of 8-colour partitions of $n$. We prove several Ramanujan type congruences modulo higher powers of 2 for the function $p_8(n)$ by finding explicit formulas for the generating functions.

math.NT↗