K. Chakraborty

activity

20172022

most citedGeneralized hypergeometric Bernoulli numbers

2 citations · 4 across the 10 of their papers we have counts for

collaborators

18 papers

math.NT2022

On a conjecture of Franu\v sić and Jadrijevi\' c: Counter-examples

Kalyan Chakraborty, Shubham Gupta, Azizul Hoque

Let $d \equiv 2 (mod 4)$ be a square-free integer such that $x^{2} - d y^{2} = - 1$ and $x^{2} - d y^{2} = 6$ are solvable in integers. We prove the existence of infinitely many quadruples in $…

math.NT2022

Lehmer sequence approach to the divisibility of class numbers of imaginary quadratic fields

Kalyan Chakraborty, Azizul Hoque

Let $k \geq 3$ and $n \geq 3$ be odd integers, and let $m \geq 0$ be any integer. For a prime number $ℓ$ , we prove that the class number of the imaginary quadratic field $\mathbb{Q…

math.NT2022

Diophantine triples with the property $D (n)$ for distinct $n$

Kalyan Chakraborty, Shubham Gupta, Azizul Hoque

We prove that for every integer $n$ , there exist infinitely many $D (n)$ -triples which are also $D (t)$ -triples for $t \in Z$ with $n \neq = t$ . We also prove that there are infin…

math.NT2022

On a family of elliptic curves of rank at least $2$

Kalyan Chakraborty, Richa Sharma

Let $C_{m} : y^{2} = x^{3} - m^{2} x + p^{2} q^{2}$ be a family of elliptic curves over $Q$ , where $m$ is a positive integer and $p, q$ are distinct odd primes. We study the…

math.NT2021

On some symmetries of the base $n$ expansion of $1/ m$ : Comments on Artin's Primitive root conjecture

Kalyan Chakraborty, Krishnarjun Krishnamoorthy

Suppose $m, n \geq 2$ are co prime integers. We prove certain new symmetries of the base $n$ representation of $1/ m$ , and in particular characterize the subgroup generated by $…

math.NT2021★ 2 cited

Generalized hypergeometric Bernoulli numbers

Kalyan Chakraborty, Takao Komatsu

We introduce generalized hypergeometric Bernoulli numbers for Dirichlet characters. We study their properties, including relations, expressions and determinants. At the end in Appe…

On a conjecture of Franu\v sić and Jadrijevi\' c: Counter-examples

Lehmer sequence approach to the divisibility of class numbers of imaginary quadratic fields

Diophantine triples with the property D(n) for distinct n

On a family of elliptic curves of rank at least 2

On some symmetries of the base n expansion of 1/m : Comments on Artin's Primitive root conjecture

Generalized hypergeometric Bernoulli numbers

Diophantine triples with the property $D (n)$ for distinct $n$

On a family of elliptic curves of rank at least $2$

On some symmetries of the base $n$ expansion of $1/ m$ : Comments on Artin's Primitive root conjecture