7 papers · 1 filter
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 .
On the simultaneous -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 . To the best of our knowledge, this is the first result…
A note on rank zero quadratic twists of a Mordell curve
Ankurjyoti Chutia, Azizul Hoque, Jyotishman Kalita
We produce two families of rank zero quadratic twists of the Mordell curve . At the end, we give numerical examples supporting the result.
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…
Parameterized families of quadratic fields with -rank at least 2
Azizul Hoque, Srinivas Kotyada
We construct parameterized families of imaginary (resp. real) quadratic fields whose class groups have -rank at least .