5 citations · 5 across the 6 of their papers we have counts for
6 papers
Rank of Pólya Groups in Lecacheux Parametric Family of Quintic Fields
Nimish Kumar Mahapatra, Prem Prakash Pandey
In this article, we study the Pólya group of a new family of quintic fields, namely Lecacheux quintic fields. We show that the associated Pólya groups can be arbitrarily large elem…
Discriminants and Large Pólya Groups in Septic Number Fields
Nimish Kumar Mahapatra
We investigate a new family of cyclic septic fields arising from the Hashimoto--Hoshi construction. For this family, we compute the discriminant explicit…
Absolutely Abelian Hilbert Class Fields and torsion conjecture
Mahesh Kumar Ram, Prem Prakash Pandey, Nimish Kumar Mahapatra
There are several recent works where authors have shown that number fields with `sufficiently many' units and cyclic class group contain a Euclidean ideal class provided the Hi…
Non-Pólya Fields with Large Pólya Groups Arising from Lehmer Quintics
Nimish Kumar Mahapatra, Prem Prakash Pandey
In this article we construct a new family of quintic non-Pólya fields with large Pólya groups. We study the upper bound of Pólya numbers of such fields and show that the Pólya numb…
Primes of higher degree and Annihilators of Class groups
Nimish Kumar Mahapatra, Prem Prakash Pandey, Mahesh Kumar Ram
Let be a Galois extension of number fields with Galois group . We discuss a new method to obtain elements in which annihilate the class group of . Using…
Small class number fields in the family
Nimish Mahapatra, Prem Prakash Pandey, Mahesh Ram
We study the class number one problem for real quadratic fields , where is an odd integer. We show that for there is only one…