K. Chakraborty

activity

20162026

most citedOn Moments of non-normal number fields

6 citations · 18 across the 21 of their papers we have counts for

collaborators

26 papers

math.CO2026

The range and omitted values of a certain sequence involving the partition function

Kalyan Chakraborty, Alisha Kazi, Manoj Upreti

Let $p(n)$ denote the ordinary partition function. Motivated by analogous questions concerning Euler's totient function and its complementary counting function, we study the rang…

math.NT2023

On the exponential Diophantine equation $x^{2} + p^{m} q^{n} = 2 y^{p}$

Kalyan Chakraborty, Azizul Hoque

We study the exponential Diophantine equation $x^{2} + p^{m} q^{n} = 2 y^{p}$ in positive integers $x, y, m, n$ , and odd primes $p$ and $q$ using primitive divisors of Lehmer sequences in combinati…

math.NT2023

Generalized Fruit Diophantine equation and Hyperelliptic curves

Om Prakash, Kalyan Chakraborty

We show the insolvability of the Diophantine equation $a x^{d} - y^{2} - z^{2} + x y z - b = 0$ in $Z$ for fixed $a$ and $b$ such that $a \equiv 1 (mod 12)$ and $b = 2^{d} a - 3$ , where $d$ is an…

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★ 5 cited

On some symmetries of the base $n$ expansion of $1/ m$ : The Class Number connection

Kalyan Chakraborty, Krishnarjun Krishnamoorthy

Suppose that $m \equiv 1 mod 4$ is a prime and that $n \equiv 3 mod 4$ is a primitive root modulo $m$ . In this paper we obtain a relation between the class number of the imagin…

math.NT2021★ 6 cited

On Moments of non-normal number fields

Kalyan Chakraborty, Krishnarjun K

Let $K$ be a number field over $Q$ and let $a_{K} (m)$ denote the number of integral ideals of $K$ of norm equal to $m \in N$ . In this paper we obtain asympt…

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…

math.NT2020

On the solutions of certain Lebesgue-Ramanujan-Nagell equations

Kalyan Chakraborty, Azizul Hoque, Richa Sharma

We completely solve the Diophantine equation $x^{2} + 2^{k} 1 1^{ℓ} 1 9^{m} = y^{n}$ in integers $x, y \geq 1; k, ℓ, m \geq 0$ and $n \geq 3$ with $g cd (x, y) = 1$ , except the case $2\mid k, 2\nmid…

math.AG2019

Divisibility of Selmer groups and class groups

Kalyan Banerjee, Kalyan Chakraborty, Azizul Hoque

In this paper, we study two topics. One is the divisibility problem of class groups of quadratic number fields and its connections to algebraic geometry. The other is the construct…

math.NT2019

Primary rank of the class group of real cyclotomic fields

Rishabh Agnihotri, Kalyan Chakraborty, Mohit Mishra

Let $H = Q (ζ_{n} + ζ_{n}^{- 1})$ and $ℓ$ be an odd prime such that $q \equiv 1 (mod ℓ)$ for some prime factor $q$ of $n$ . We get a bound on the $ℓ$ -rank of the cl…

math.NT2019

Selmer group associated to the Chow group of certain codimension two cycles

Kalyan Banerjee, Kalyan Chakraborty

Let $X$ be a surface with geometric genus and irregularity zero which is defined over a number field $K$ . Let $X$ denote a smooth spread of $X$ over the spectrum of a Zar…

math.NT2019

On a question of Colliot-Thélène on Chow group mod $n$

Kalyan Banerjee, Kalyan Chakraborty

In this note we define the notion of Tate-Shafarevich group and Selmer group of the Chow group of an abelian variety defined over a number field. In this context we give positive a…

math.NT2019

On the structure of order 4 class groups of $Q (n^{2} + 1)$

Kalyan Chakraborty, Azizul Hoque, Mohit Mishra

Groups of order $4$ are isomorphic to either $Z /4 Z$ or $Z /2 Z \times Z /2 Z$ . We give certain sufficient conditions permitting to…

math.NT2018

Complete solutions of certain Lebesgue-Ramanujan-Nagell type equations

Kalyan Chakraborty, Azizul Hoque, Richa Sharma

It is well-known that for $p = 1, 2, 3, 7, 11, 19, 43, 67, 163$ , the class number of $Q (- p)$ is one. We use this fact to determine all the solutions of $x^{2} + p^{m} = 4 y^{n}$ …

math.NT2018★ 2 cited

A note on certain real quadratic fields with class number upto three

Kalyan Chakraborty, Azizul Hoque, Mohit Mishra

We obtain criteria for the class number of certain Richaud-Degert type real quadratic fields to be 3. We also treat a couple of families of real quadratic fields of Richaud-Degert…

math.NT2018★ 1 cited

Class groups of imaginary quadratic fields of $3$ -rank at least $2$

Kalyan Chakraborty, Azizul Hoque

We produce an infinite family of imaginary quadratic fields whose ideal class groups have $3$ -rank at least $2$ .

math.NT2018

Exponents of class groups of certain imaginary quadratic fields

Kalyan Chakraborty, Azizul Hoque

Let $n > 1$ be an odd integer. We prove that there are infinitely many imaginary quadratic fields of the form $Q (x^{2} - 2 y^{n})$ whose ideal class group has an element of…

math.NT2017★ 2 cited

Divisibility of class numbers of certain families of quadratic fields

Azizul Hoque, Kalyan Chakraborty

We construct some families of quadratic fields whose class numbers are divisible by $3.$ The main tools used are a trinomial introduced by Kishi and a parametrization of Kishi and…

math.NT2017

Pell-type equations and class number of the maximal real subfield of a cyclotomic field

Azizul Hoque, Kalyan Chakraborty

We investigate the solvability of the Diophantine equation $x^{2} - m y^{2} = \pm p$ in integers for certain integer $m$ and prime $p$ . Then we apply these results to produce family of maxi…

math.NT2017

Quadratic reciprocity and Some "non-differentiable" functions

Kalyan Chakraborty, Azizul Hoque

Riemann's non-differentiable function and Gauss's quadratic reciprocity law have attracted the attention of many researchers. In \cite{RM} Murty and Pacelli gave an instructive pro…

The range and omitted values of a certain sequence involving the partition function

On the exponential Diophantine equation x2+pmqn=2yp

Generalized Fruit Diophantine equation and Hyperelliptic curves

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

On some symmetries of the base n expansion of 1/m : The Class Number connection

On Moments of non-normal number fields

Generalized hypergeometric Bernoulli numbers

On the solutions of certain Lebesgue-Ramanujan-Nagell equations

Divisibility of Selmer groups and class groups

Primary rank of the class group of real cyclotomic fields

Selmer group associated to the Chow group of certain codimension two cycles

On a question of Colliot-Thélène on Chow group mod n

On the structure of order 4 class groups of Q(n2+1​)

Complete solutions of certain Lebesgue-Ramanujan-Nagell type equations

A note on certain real quadratic fields with class number upto three

Class groups of imaginary quadratic fields of 3-rank at least 2

Exponents of class groups of certain imaginary quadratic fields

Divisibility of class numbers of certain families of quadratic fields

Pell-type equations and class number of the maximal real subfield of a cyclotomic field

Quadratic reciprocity and Some "non-differentiable" functions

On the exponential Diophantine equation $x^{2} + p^{m} q^{n} = 2 y^{p}$

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

On some symmetries of the base $n$ expansion of $1/ m$ : The Class Number connection

On a question of Colliot-Thélène on Chow group mod $n$

On the structure of order 4 class groups of $Q (n^{2} + 1)$

Class groups of imaginary quadratic fields of $3$ -rank at least $2$