Rupam Barman

activity

20122026

most citedOn Andrews' integer partitions with even parts below odd parts

17 citations · 40 across the 41 of their papers we have counts for

collaborators

Showing 2023 · math.NTShow all

7 papers · 2 filters

math.NT2023

$p$ -Adic hypergeometric functions and the trace of Frobenius of elliptic curves

Sulakashna, Rupam Barman

Let $p$ be an odd prime and $q = p^{r}$ , $r \geq 1$ . For positive integers $n$ , let $_{n} G_{n} [\dots]_{q}$ denote McCarthy's $p$ -adic hypergeometric functions. In this article, we prove an…

math.NT2023

Arithmetic properties and asymptotic formulae for $σ_{o} mex (n)$ and $σ_{e} mex (n)$

Gurinder Singh, Rupam Barman

The minimal excludant of an integer partition is the least positive integer missing from the partition. Let $σ_{o} mex (n)$ (resp., $σ_{e} mex (n)$ ) denote the sum of odd (re…

math.NT2023

On $p$ -adic denseness of quotients of values of integral forms

Deepa Antony, Rupam Barman, Stevan Gajović +1

Given $A \subseteq Z$ , the ratio set or the quotient set of $A$ is defined by $R (A) := {a / b : a, b \in A, b \neq = 0}$ . It is an open problem to study the denseness of $R (A)$ in the $p$ …

math.NT2023

Diagonal hypersurfaces and elliptic curves over finite fields and hypergeometric functions

Sulakashna, Rupam Barman

Let $D_{λ}^{d, k}$ denote the family of diagonal hypersurface over a finite field $F_{q}$ given by \begin{align*} D_λ^{d,k}:X_1^d+X_2^d=λdX_1^kx_2^{d-k}, \end{align*} where $d\…

math.NT2023

Congruences for the partition function $PDO_{t} (n)$ modulo powers of $2$ and $3$

Gurinder Singh, Rupam Barman

Lin introduced the partition function $PDO_{t} (n)$ , which counts the total number of tagged parts over all the partitions of $n$ with designated summands in which all parts ar…

math.NT2023

Parity distribution and divisibility of Mex-related partition functions

Subhrajyoti Bhattacharyya, Rupam Barman, Ajit Singh +1

Andrews and Newman introduced the mex-function $mex_{A, a} (λ)$ for an integer partition $λ$ of a positive integer $n$ as the smallest positive integer congruent to $a$ modulo…

p-Adic hypergeometric functions and the trace of Frobenius of elliptic curves

Arithmetic properties and asymptotic formulae for σo​mex(n) and σe​mex(n)

On p-adic denseness of quotients of values of integral forms

Diagonal hypersurfaces and elliptic curves over finite fields and hypergeometric functions

Congruences for the partition function PDOt​(n) modulo powers of 2 and 3

Parity distribution and divisibility of Mex-related partition functions

$p$ -Adic hypergeometric functions and the trace of Frobenius of elliptic curves

Arithmetic properties and asymptotic formulae for $σ_{o} mex (n)$ and $σ_{e} mex (n)$

On $p$ -adic denseness of quotients of values of integral forms

Congruences for the partition function $PDO_{t} (n)$ modulo powers of $2$ and $3$