Rupam Barman

activity

20122025

most citedCertain product formulas and values of Gaussian hypergeometric series

8 citations · 12 across the 15 of their papers we have counts for

collaborators

Showing math.NTShow all

21 papers · 1 filter

math.NT2022★ 1 cited

Number of $F_{q}$ -points on Diagonal hypersurfaces and hypergeometric function

Sulakashna, Rupam Barman

Let $D_{λ}^{d}$ denote the family of monomial deformations of diagonal hypersurface over a finite field $F_{q}$ given by \begin{align*} D_λ^d: X_1^d+X_2^d+\cdots+X_n^d=λd X_1^{h…

math.NT2022

Certain transformations and values of p-adic hypergeometric functions

Sulakashna, Rupam Barman

We prove two transformations for the $p$ -adic hypergeometric functions which can be described as $p$ -adic analogues of a Euler's transformation and a transformation of Clausen. We…

math.NT2022

Proofs of some conjectures of Keith and Zanello on $t$ -regular partition

Ajit Singh, Rupam Barman

For a positive integer $t$ , let $b_{t} (n)$ denote the number of $t$ -regular partitions of a nonnegative integer $n$ . In a recent paper, Keith and Zanello established infinite famil…

math.NT2022

$p$ -Adic quotient sets: diagonal forms

Deepa Antony, Rupam Barman, Piotr Miska

For a set of integers $A$ , we consider $R (A) = {a / b : a, b \in A, b \neq = 0}$ . It is an open problem to study the denseness of $R (A)$ in the $p$ -adic numbers when $A$ is the set of non…

math.NT2021

Proof of some conjectural congruences of da Silva and Sellers

Ajit Singh, Rupam Barman

Let $p_{{3, 3}} (n)$ denote the number of $3$ -regular partitions in three colours. In a very recent paper, da Silva and Sellers studied certain arithmetic properties of $p_{\{3, 3…

math.NT2021

Divisibility of certain $ℓ$ -regular partitions by $2$

Ajit Singh, Rupam Barman

For a positive integer $ℓ$ , let $b_{ℓ} (n)$ denote the number of $ℓ$ -regular partitions of a nonnegative integer $n$ . Motivated by some recent conjectures of Keith and Zane…

Number of Fq​-points on Diagonal hypersurfaces and hypergeometric function

Certain transformations and values of p-adic hypergeometric functions

Proofs of some conjectures of Keith and Zanello on t-regular partition

p-Adic quotient sets: diagonal forms

Proof of some conjectural congruences of da Silva and Sellers

Divisibility of certain ℓ-regular partitions by 2

Number of $F_{q}$ -points on Diagonal hypersurfaces and hypergeometric function

Proofs of some conjectures of Keith and Zanello on $t$ -regular partition

$p$ -Adic quotient sets: diagonal forms

Divisibility of certain $ℓ$ -regular partitions by $2$