Azizul Hoque

activity

20162026

most citedA note on certain real quadratic fields with class number upto three

2 citations · 7 across the 23 of their papers we have counts for

collaborators

30 papers

math.NT2026

Branched covers of $P^{1}$ and divisibility in class group

Kalyan Banerjee, Kalyan Chakraborty, Azizul Hoque

We start with $n$ -torsions in the Jacobian of an $m$ -gonal curve and produce $n$ -torsions in the class group of certain number field $K$ .

math.NT2025

On the simultaneous $3$ -divisibility of class numbers of quadruples of real quadratic fields

Kalyan Banerjee, Ankurjyoti Chutia, Azizul Hoque

In this paper, we construct infinitely many quadruples of real quadratic fields whose class numbers are all divisible by $3$ . To the best of our knowledge, this is the first result…

math.NT2025

Elliptic surfaces to class groups and Selmer groups

Kalyan Banerjee, Kalyan Chakraborty, Azizul Hoque

In this note, we connect the $n$ -torsions of the Picard group of an elliptic surface to the $n$ -divisibility of the class group of torsion fields for a given integer $n > 1$ . We also…

math.NT2025

Fields with small class group in the family $Q (9 m^{2} + 2 m)$

Kalyan Chakraborty, Azizul Hoque

Very recently, Issa and Darrag [Arch. Math. (Basel) 123 (2024), no. 4, 379-383] determined partial Dedekind zeta values for certain ideal classes in the real quadratic fields of th…

math.NT2024

Parameterized families of quadratic fields with $n$ -rank at least 2

Azizul Hoque, Srinivas Kotyada

We construct parameterized families of imaginary (resp. real) quadratic fields whose class groups have $n$ -rank at least $2$ .

math.NT2023★ 1 cited

On the plus parts of the class numbers of cyclotomic fields

Kalyan Chakraborty, Azizul Hoque

We exhibit some new families of cyclotomic fields which have non-trivial plus parts of their class numbers. We also prove the $3$ - divisibility of the plus part of the class numbe…

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

Diophantine $D (n)$ -quadruples in $Z [4 k + 2]$

Kalyan Chakraborty, Shubham Gupta, Azizul Hoque

Let $d$ be a square-free integer and $Z [d]$ a quadratic ring of integers. For a given $n \in Z [d]$ , a set of $m$ non-zero distinct elements in $\mathb…

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.NT2021

On the Diophantine equation $d x^{2} + p^{2 a} q^{2 b} = 4 y^{p}$

Kalyan Chakraborty, Azizul Hoque

We investigate the solvability of the Diophantine equation in the title, where $d > 1$ is a square-free integer, $p, q$ are distinct odd primes and $x, y, a, b$ are unknown positive int…

math.NT2021

On the Diophantine equation $c x^{2} + p^{2 m} = 4 y^{n}$

Kalyan Chakraborty, Azizul Hoque, Kotyada Srinivas

Let $c$ be a square-free positive integer and $p$ a prime satisfying $p ∤ c$ . Let $h (- c)$ denote the class number of the imaginary quadratic field $Q (- c)$ . In th…

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.NT2020

Class number one problem for the real quadratic fields $Q (m^{2} + 2 r)$

Azizul Hoque, Srinivas Kotyada

We investigate the class number one problem for a parametric family of real quadratic fields of the form $Q (m^{2} + 4 r)$ for certain positive integers $m$ and $r$ .

math.NT2020

On the exponents of class groups of some families of imaginary quadratic fields

Azizul Hoque

Let $a \geq 1$ and $n > 1$ be odd integers. For a given prime $p$ , we prove under certain conditions that the class groups of imaginary quadratic fields $Q (a^{2} - 4 p^{n})$ …

math.NT2020

On a class of Lebesgue-Ramanujan-Nagell equations

Azizul Hoque

We deeply investigate the Diophantine equation $c x^{2} + d^{2 m + 1} = 2 y^{n}$ in integers $x, y \geq 1, m \geq 0$ and $n \geq 3$ , where $c$ and $d$ are given coprime positive integers such that…

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.RA2019

Some aspects of quasi-pseudo principally injective modules

Hemen Dutta, Azizul Hoque, Samer M. Saeed

In this paper, the notion of quasi-pseudo injectivity relative to a class of submodules, namely, quasi-pseudo principally injective has been studied. This notion is closed under di…

math.AG2019

Picard groups, pull back and class groups

Kalyan Banerjee, Azizul Hoque

Let $S$ be a certain affine algebraic surface over $Q$ such that it admits a regular map to $A^{2} / Q$ . We show that any non-trivial torsion line bundle in…

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

On the solutions of a Lebesgue - Nagell type equation

Sanjay Bhatter, Azizul Hoque, Richa Sharma

We find all positive integer solutions in $x, y$ and $n$ of $x^{2} + 1 9^{2 k + 1} = 4 y^{n}$ for any non-negative integer $k$ .

math.NT2018★ 1 cited

Cyoclotomic Numbers Of Order 2l^2 With Prime L

Md. Helal Ahmed, Jagmohan Tanti, Azizul Hoque

The problem of determining cyclotomic numbers in terms of the solutions of certain Diophantine systems has been treated by many authors since the age of Gauss. In this paper we obt…

Branched covers of P1 and divisibility in class group

On the simultaneous 3-divisibility of class numbers of quadruples of real quadratic fields

Elliptic surfaces to class groups and Selmer groups

Fields with small class group in the family Q(9m2+2m​)

Parameterized families of quadratic fields with n-rank at least 2

On the plus parts of the class numbers of cyclotomic fields

On the exponential Diophantine equation x2+pmqn=2yp

Diophantine D(n)-quadruples in Z[4k+2​]

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

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

On the Diophantine equation dx2+p2aq2b=4yp

On the Diophantine equation cx2+p2m=4yn

On the solutions of certain Lebesgue-Ramanujan-Nagell equations

Class number one problem for the real quadratic fields Q(m2+2r​)

On the exponents of class groups of some families of imaginary quadratic fields

On a class of Lebesgue-Ramanujan-Nagell equations

Divisibility of Selmer groups and class groups

Some aspects of quasi-pseudo principally injective modules

Picard groups, pull back and class groups

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

On the solutions of a Lebesgue - Nagell type equation

Cyoclotomic Numbers Of Order 2l^2 With Prime L

Branched covers of $P^{1}$ and divisibility in class group

On the simultaneous $3$ -divisibility of class numbers of quadruples of real quadratic fields

Fields with small class group in the family $Q (9 m^{2} + 2 m)$

Parameterized families of quadratic fields with $n$ -rank at least 2

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

Diophantine $D (n)$ -quadruples in $Z [4 k + 2]$

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

On the Diophantine equation $d x^{2} + p^{2 a} q^{2 b} = 4 y^{p}$

On the Diophantine equation $c x^{2} + p^{2 m} = 4 y^{n}$

Class number one problem for the real quadratic fields $Q (m^{2} + 2 r)$

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