Nabin Kumar Meher

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math.NT2025

On the number of irreducible representations of $\so(5)$

Saudamini Nayak, Nabin Kumar Meher, Sudhansu Sekhar Rout

Let $d (n)$ be the divisor function and it is well known that $\sum_{1 \leq n \leq x} d (n) = x lo g x + (2 γ - 1) x + O (x^{θ + ε})$ where $γ$ is the Euler constant, $ε > 0$ a…

math.NT2024★ 1 cited

Distribution and congruences of $(u, v)$ -regular bipartitions

Nabin Kumar Meher

Let $B_{u, v} (n)$ denote the number of $(u, v)$ -regular bipartitions of $n$ . In this article, we prove that $B_{p, m} (n)$ is always almost divisible by $p,$ where $p \geq 5$ is a prime…

math.NT2024

Arithmetic density and congruences of $ℓ$ -regular bipartitions $I I$

Nabin Kumar Meher

Let $B_{ℓ} (n)$ denote the number of $ℓ -$ regular bipartitions of $n .$ In 2013, Lin \cite{Lin2013} proved a density result for $B_{4} (n) .$ He showed that for any positive intege…

math.NT2024

Arithmetic density and congruences of $ℓ$ -regular bipartitions

Nabin Kumar Meher, Ankita Jindal

Let $B_{ℓ} (n)$ denote the number of $ℓ$ -regular bipartitions of $n .$ In this article, we prove that $B_{ℓ} (n)$ is always almost divisible by $p_{i}^{j}$ if $p_i^{2a_i}\geq \…

math.NT2023

Analytic continuation of $ℓ$ -generalized Fibonacci zeta function

Dilip Kumar Sahoo, Nabin Kumar Meher

In this paper, for any positive integer $ℓ \geq 2,$ we define $ℓ$ -generalized Fibonacci zeta function. We then study its analytic continuation to the whole complex plane $\math…

math.NT2023

Infinite families of congruences for $2$ and $13$ -core partitions

Ankita Jindal, Nabin Kumar Meher

A partition of $n$ is called a $t$ -core partition if none of its hook number is divisible by $t .$ In 2019, Hirschhorn and Sellers \cite{Hirs2019} obtained a parity result for $3$ -c…

On the number of irreducible representations of $\so(5)$

Distribution and congruences of (u,v)-regular bipartitions

Arithmetic density and congruences of ℓ-regular bipartitions II

Arithmetic density and congruences of ℓ-regular bipartitions

Analytic continuation of ℓ-generalized Fibonacci zeta function

Infinite families of congruences for 2 and 13-core partitions

Distribution and congruences of $(u, v)$ -regular bipartitions

Arithmetic density and congruences of $ℓ$ -regular bipartitions $I I$

Arithmetic density and congruences of $ℓ$ -regular bipartitions

Analytic continuation of $ℓ$ -generalized Fibonacci zeta function

Infinite families of congruences for $2$ and $13$ -core partitions