5 citations · 5 across the 13 of their papers we have counts for
14 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…
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…
Primes of Higher Degree
Prem Prakash Pandey, Mahesh Kumar Ram
Let $K/\Q$ be a cyclic extension of number fields with Galois group . We study the ideal classes of primes of of residue degree bigger than one in the class g…
Square-free values of polynomials
Prem Prakash Pandey
It is conjectured that all separable polynomials with integers coefficients, satisfying some local conditions, take infinitely many square free values on integer arguments. But not…
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…
Divisibility of the class numbers of imaginary quadratic fields
Kalyan Chakraborty, Azizul Hoque, Yasuhiro Kishi +1
For a given odd integer , we provide some families of imaginary quadratic number fields of the form whose ideal class group has a subgroup isomorp…
Distribution of prime ideals of higher residue degree across ideal classes in the class groups
Prem Prakash Pandey
In this article we investigate the distribution of prime ideals of residue degree bigger than one across the ideal classes in the class group of a number field . A criterion for…
On Freiman's 3k-4 theorem
R. Balasubramanian, Prem Prakash Pandey
One of the many theorems Freiman proved, in the second half of the twentieth century, in the subject which later came to be known as "structure theory of set addition", was 'Freima…
On a Theorem of Deshouillers and Freiman
R. Balasubramanian, Prem Prakash Pandey
The study of `structure' on subsets of abelian groups, with small `doubling constant', has been well studied in the last fifty years, from the time Freiman initiated the subject. I…
Catalan's Equation For Even Primes over Quadratic Fields
R. Balasubramanian, Prem Prakash Pandey
This article lists all the solution of the Catalan equation for , when one of the primes is even.
Higher Residue Symbol
R. Balasubramanian, Prem Prakash Pandey
Given a prime number and a finite set of integers we find out the exact degree of the extension $\mathbb{Q}(a_1^{\frac{1}{l}},...,a_m^{\frac{1}{l}})/\mathbb…
Higher residue symbols
R. Balasubramanian, Prem Prakash Pandey
Given a prime number and a finite set of integers we find out the exact degree of the extension $\mathbb{Q}(a_1^{\frac{1}{l}},...,a_m^{\frac{1}{l}})/\mathbb…