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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…