1 citations · 1 across the 8 of their papers we have counts for
11 papers
An infinite family of imaginary biquadratic fields with a large class number
Kalyan Chakraborty, Pratik Rao, Aishwarya Dabhole
We construct an infinite family of imaginary biquadratic fields with large class numbers. The construction of this family is done by composing two distinct families of imaginary qu…
On the class number of certain cyclotomic fields
Kalyan Chakraborty, Pratik Rao
We construct four infinite families of cyclotomic fields and show that each member of these families has class number a multiple of 3. In fact, we show that the class number of the…
Branched covers of and divisibility in class group
Kalyan Banerjee, Kalyan Chakraborty, Azizul Hoque
We start with -torsions in the Jacobian of an -gonal curve and produce -torsions in the class group of certain number field .
Diophantine tuples and Integral Ideals of
Kalyan Chakraborty, Shubham Gupta, Krishnarjun Krishnamoorthy
Suppose is the fundamental discriminant associated with a quadratic extension of . We show that for every Diophantine -tuple with t…
Elliptic surfaces to class groups and Selmer groups
Kalyan Banerjee, Kalyan Chakraborty, Azizul Hoque
In this note, we connect the -torsions of the Picard group of an elliptic surface to the -divisibility of the class group of torsion fields for a given integer . We also…
Fields with small class group in the family
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…
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 - divisibility of the plus part of the class numbe…
Diophantine -quadruples in
Kalyan Chakraborty, Shubham Gupta, Azizul Hoque
Let be a square-free integer and a quadratic ring of integers. For a given , a set of non-zero distinct elements in $\mathb…
On the Diophantine equation
Kalyan Chakraborty, Azizul Hoque
We investigate the solvability of the Diophantine equation in the title, where is a square-free integer, are distinct odd primes and are unknown positive int…
On the complete solutions of a generalized Lebesgue-Ramanujan-Nagell equation
Kalyan Chakraborty, Azizul Hoque
We consider the generalized Lebesgue-Ramanujan-Nagell equation in the unknown integers and satisfying $\gcd(…
On the Diophantine equation
Kalyan Chakraborty, Azizul Hoque, Kotyada Srinivas
Let be a square-free positive integer and a prime satisfying . Let denote the class number of the imaginary quadratic field . In th…