Azizul Hoque

activity

20172022

most citedDivisibility of class numbers of certain families of quadratic fields

2 citations · 2 across the 5 of their papers we have counts for

collaborators

14 papers

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.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.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…

On the Diophantine equation cx2+p2m=4yn