Rupam Barman

activity

20122019

collaborators

6 papers

math.NT2019

Divisibility of Andrews' Singular Overpartitions by Powers of 2 and 3

Rupam Barman, Chiranjit Ray

Andrews introduced the partition function $C_{k, i} (n)$ , called singular overpartition, which counts the number of overpartitions of $n$ in which no part is divisible by…

math.NT2018

A finite field analogue of the Appell series $F_{4}$

Mohit Tripathi, Rupam Barman

We define a function $F_{4}^{*}$ as a finite field analogue of the classical Appell series $F_{4}$ using Gauss sums. We establish identities for $F_{4}^{*}$ analogous to those sati…

math.NT2016

Proof of a Limited Version of Mao's Partition Rank Inequality using a Theta Function Identity

Rupam Barman, Archit Pal Singh Sachdeva

Ramanujan's congruence $p (5 k + 4) \equiv 0 (mod 5)$ led Dyson \cite{dyson} to conjecture the existence of a measure "rank" such that $p (5 k + 4)$ partitions of $5 k + 4$ could be divided i…

math.NT2012

Hypergeometric functions over $F_{q}$ and traces of Frobenius for elliptic curves

Rupam Barman, Gautam Kalita

We present here explicit relations between the traces of Frobenius endomorphisms of certain families of elliptic curves and special values of $_{2} F_{1}$ -hypergeometric functions o…

math.NT2012

Certain values of Gaussian hypergeometric series and a family of algebraic curves

Rupam Barman, Gautam Kalita

Let $λ \in Q ∖ {0, - 1}$ and $l \geq 2$ . Denote by $C_{l, λ}$ the nonsingular projective algebraic curve over $Q$ with affine equation given by $$y^l=(x-1)(…

math.NT2012

Hypergeometric functions and a family of algebraic curves

Rupam Barman, Gautam Kalita

Let $λ \in Q ∖ {0, 1}$ and $l \geq 2$ , and denote by $C_{l, λ}$ the nonsingular projective algebraic curve over $Q$ with affine equation given by $$y^l=x(x…

Divisibility of Andrews' Singular Overpartitions by Powers of 2 and 3

A finite field analogue of the Appell series F4​

Proof of a Limited Version of Mao's Partition Rank Inequality using a Theta Function Identity

Hypergeometric functions over Fq​ and traces of Frobenius for elliptic curves

Certain values of Gaussian hypergeometric series and a family of algebraic curves

Hypergeometric functions and a family of algebraic curves

A finite field analogue of the Appell series $F_{4}$

Hypergeometric functions over $F_{q}$ and traces of Frobenius for elliptic curves