Jaitra Chattopadhyay

activity

20182026

collaborators

22 papers

math.GM2026

Representation of similar triangles in $R^{3}$

Jaitra Chattopadhyay, Siddhartha Sankar Chattopadhyay

In 1994, Dhar and Sinha provided a graphic representation in $R^{2}$ of the classification of triangles based on similarity. In this article, we briefly recall their treat…

math.NT2026

Two infinite families of elliptic curves with Mordell-Weil rank at least $3$

Pankaj Patel, Debopam Chakraborty, Jaitra Chattopadhyay

In this paper, we consider two infinite parametric families of elliptic curves defined over $Q$ given by the equations $E_{a, b} : y^{2} = x^{3} - a^{2} x + b^{2}$ and $E^{\…

math.NT2025

Some bi-quadratic Pólya fields and large Pólya groups of compositum of simplest cubic and quintic fields

Md. Imdadul Islam, Debopam Chakraborty, Jaitra Chattopadhyay

The Pólya group $P o (K)$ of an algebraic number field $K$ is the subgroup of the ideal class group $C l_{K}$ generated by the ideal classes of the products of prime ideals of the sam…

math.NT2025

On the Mordell-Weil rank and $2$ -Selmer group of a family of elliptic curves

Pankaj Patel, Debopam Chakraborty, Jaitra Chattopadhyay

We consider the parametric family of elliptic curves over $Q$ of the form $E_{m} : y^{2} = x (x - n_{1}) (x - n_{2}) + t^{2}$ , where $n_{1}$ , $n_{2}$ and $t$ are particular…

math.NT2024

Bi-quadratic Pólya fields with five distinct ramified primes

Md. Imdadul Islam, Jaitra Chattopadhyay, Debopam Chakraborty

For an algebraic number field $K$ , the Pólya group of $K$ , denoted by $P o (K),$ is the subgroup of the ideal class group $C l_{K}$ generated by the ideal classes of the products of p…

math.NT2023

Large Pólya groups in simplest cubic fields and consecutive bi-qaudratic fields

Md. Imdadul Islam, Jaitra Chattopadhyay, Debopam Chakraborty

The Pólya group of an algebraic number field is the subgroup generated by the ideal classes of the products of prime ideals of equal norm inside the ideal class group. Inspired by…

math.NT2023

A brief survey of recent results on Pólya groups

Jaitra Chattopadhyay, Anupam Saikia

The Pólya group of an algebraic number field is a particular subgroup of the ideal class group. This article provides an overview of recent results on Pólya groups of number fields…

math.NT2023

On the structure and stability of ranks of $2$ -class groups in cyclotomic $Z_{2}$ -extensions of certain real quadratic fields

Jaitra Chattopadhyay, H Laxmi, Anupam Saikia

For a real quadratic field $K = Q (d)$ with discriminant $D_{K}$ having four distinct prime factors, we study the structure of the $2$ -class group $A (K_{1})$ of the f…

math.NT2022

On the $p$ -rationality of consecutive quadratic fields

Jaitra Chattopadhyay, H Laxmi, Anupam Saikia

In 2016, in the work related to Galois representations, Greenberg conjectured the existence of multi-quadratic $p$ -rational number fields of degree $2^{t}$ for any odd prime number…

math.NT2022

On denseness of certain direction and generalized direction sets

Deepa Antony, Rupam Barman, Jaitra Chattopadhyay

Direction sets, recently introduced by Leonetti and Sanna, are generalization of ratio sets of subsets of positive integers. In this article, we generalize the notion of direction…

math.NT2021

On the $p$ -ranks of the ideal class groups of imaginary quadratic fields

Jaitra Chattopadhyay, Anupam Saikia

For a prime number $p \geq 5$ , we explicitly construct a family of imaginary quadratic fields $K$ with ideal class groups $C l_{K}$ having $p$ -rank $rk_{p} (C l_{K})$ at least…

math.NT2021

Totally real bi-quadratic fields with large Pólya groups

Jaitra Chattopadhyay, Anupam Saikia

For an algebraic number field $K$ with ring of integers $O_{K}$ , an important subgroup of the ideal class group $C l_{K}$ is the {\it Pólya group}, denoted by $P o (K)$ , whi…

math.NT2021

Non-Pólya bi-quadratic fields with an Euclidean ideal class

Jaitra Chattopadhyay, Anupam Saikia

For an integral domain $R$ , the {\it ring of integer-valued polynomials} over $R$ consists of all polynomials $f (X) \in R [X]$ such that $f (R) \subseteq R$ . An interesting case to s…

math.NT2020

Simultaneous indivisibility of class numbers of pairs of real quadratic fields

Jaitra Chattopadhyay, Anupam Saikia

For a square-free integer $t$ , Byeon \cite{byeon} proved the existence of infinitely many pairs of quadratic fields $Q (D)$ and $Q (t D)$ with $D > 0$ …

math.NT2020

On a generalization of Menon-Sury identity to number fields involving a Dirichlet Character

Jaitra Chattopadhyay, Subha Sarkar

For every positive integer $n$ , Sita Ramaiah's identity states that \medskip \begin{equation*} \sum_{a_1, a_2, a_1+a_2 \in (\mathbb{Z}/n\mathbb{Z})^*} \gcd(a_1+a_2-1,n) = ϕ_2(n)σ_0…

math.NT2019

On the simultaneous $3$ -divisibility of class numbers of triples of imaginary quadratic fields

Jaitra Chattopadhyay, Subramani Muthukrishnan

Let $k \geq 1$ be a cube-free integer with $k \equiv 1 (mod 9)$ and $g cd (k, 7 \cdot 571) = 1$ . In this paper, we prove the existence of infinitely many triples of imaginary quadrat…

math.NT2018

Mean values and moments of arithmetic functions over number fields

Jaitra Chattopadhyay, Pranendu Darbar

For an odd integer $d > 1$ and a finite Galois extension $K / Q$ of degree $d$ , G. Lü and Z. Yang \cite{lu3} obtained an asymptotic formula for the mean values of the diviso…

math.NT2018

Distribution of residues modulo $p$ using the Dirichlet's class number formula

Jaitra Chattopadhyay, Bidisha Roy, Subha Sarkar +1

Let $p$ be an odd prime number. In this article, we study the number of quadratic residues and non-residues modulo $p$ which are multiples of $2$ or $3$ or $4$ and lying in the int…

math.NT2018

Biquadratic fields having a non-principal euclidean ideal class

Jaitra Chattopadhyay, Subramani Muthukrishnan

H. W. Lenstra \cite{lenstra} introduced the notion of an Euclidean ideal class, which is a generalization of norm-Euclidean ideals in number fields. Later, families of number field…

math.NT2018

Quadratic non-residues and non-primitive roots satisfying a coprimality condition

Jaitra Chattopadhyay, Bidisha Roy, Subha Sarkar +1

Let $q \geq 1$ be any integer and let $ε \in [\frac{1}{11}, \frac{1}{2})$ be a given real number. In this short note, we prove that for all primes $p$ satisfying $$ p\equiv 1\pmod{q…

math.NT2018

A short note on the divisibility of class numbers of real quadratic fields

Jaitra Chattopadhyay

For any integer $l \geq 1$ , let $p_{1}, p_{2}, \dots, p_{l + 2}$ be distinct prime numbers $\geq 5.$ For all real numbers $X > 1,$ we let $N_{3, l} (X)$ denote the number of real quadratic f…

math.NT2018

On Fractionally Dense Sets

Jaitra Chattopadhyay, Bidisha Roy, Subha Sarkar

In this article, we prove some subsets of the set of natural numbers $N$ and any non-zero ideals of an order of imaginary quadratic fields are fractionally dense in $\math…

Representation of similar triangles in R3

Two infinite families of elliptic curves with Mordell-Weil rank at least 3

Some bi-quadratic Pólya fields and large Pólya groups of compositum of simplest cubic and quintic fields

On the Mordell-Weil rank and 2-Selmer group of a family of elliptic curves

Bi-quadratic Pólya fields with five distinct ramified primes

Large Pólya groups in simplest cubic fields and consecutive bi-qaudratic fields

A brief survey of recent results on Pólya groups

On the structure and stability of ranks of 2-class groups in cyclotomic Z2​-extensions of certain real quadratic fields

On the p-rationality of consecutive quadratic fields

On denseness of certain direction and generalized direction sets

On the p-ranks of the ideal class groups of imaginary quadratic fields

Totally real bi-quadratic fields with large Pólya groups

Non-Pólya bi-quadratic fields with an Euclidean ideal class

Simultaneous indivisibility of class numbers of pairs of real quadratic fields

On a generalization of Menon-Sury identity to number fields involving a Dirichlet Character

On the simultaneous 3-divisibility of class numbers of triples of imaginary quadratic fields

Mean values and moments of arithmetic functions over number fields

Distribution of residues modulo p using the Dirichlet's class number formula

Biquadratic fields having a non-principal euclidean ideal class

Quadratic non-residues and non-primitive roots satisfying a coprimality condition

A short note on the divisibility of class numbers of real quadratic fields

On Fractionally Dense Sets

Representation of similar triangles in $R^{3}$

Two infinite families of elliptic curves with Mordell-Weil rank at least $3$

On the Mordell-Weil rank and $2$ -Selmer group of a family of elliptic curves

On the structure and stability of ranks of $2$ -class groups in cyclotomic $Z_{2}$ -extensions of certain real quadratic fields

On the $p$ -rationality of consecutive quadratic fields

On the $p$ -ranks of the ideal class groups of imaginary quadratic fields

On the simultaneous $3$ -divisibility of class numbers of triples of imaginary quadratic fields

Distribution of residues modulo $p$ using the Dirichlet's class number formula