Md. Imdadul Islam

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20232025

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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.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

Quadratic Twists of Heronian Elliptic Curves with Arbitrarily Large 2-Selmer Rank

Vinodkumar Ghale, Md Imdadul Islam

This paper explicitly determines the 2-Selmer group of the family of elliptic curves arising from Heron triangles of area 2mn. By analyzing the quadratic twists induced by powers o…