R. Kalwaniya

activity

20232026

most citedA Study of monogenity of Binomial Composition

1 citations · 2 across the 8 of their papers we have counts for

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math.NT2026

On The Index of Polynomial Compositions over Valued Fields

Anuj Jakhar, Ravi Kalwaniya, Shanta Laishram +1

Determining whether an algebraic number field admits a power integral basis is a classical problem, but it can be difficult for fields defined by polynomial compositions and dynami…

math.NT2026

A Deterministic Cryptographic Prime Generation Chain over Monogenic Cubic Number Fields and their Generalizations

Anuj Jakhar, Ravi Kalwaniya

Generating primes is a fundamental problem in modern cryptography. Deterministic primality tests work well for special integers such as Mersenne or Proth primes, but these forms ar…

math.NT2026

Monogenic Fields from Polynomial Compositions with Applications

Anuj Jakhar, Ravi Kalwaniya, Prabhakar Yadav

A number field $K$ is called \emph{monogenic} if its ring of integers $Z_{K}$ can be expressed as a simple ring extension $Z [α]$ for some $α \in Z_{K}$ . A mon…

math.NT2026

Arithmetic Aspects of Number Fields Generated by Polynomial Families

Rupam Barman, Anuj Jakhar, Ravi Kalwaniya +1

Let $f (x) = (x^{k} + c)^{m} - a x^{n} \in Z [x]$ be an irreducible polynomial over $Q$ , where $k, m, n \in N$ with $k m > n$ , and let $K = Q (θ)$ , where $θ$ is a ro…

math.NT2026

On the distribution of shapes of sextic pure number fields

Anuj Jakhar, Ravi Kalwaniya, Anwesh Ray +1

The shape of a number field $K$ of degree $n$ is defined as the equivalence class of the lattice of integers with respect to linear operations that are composites of rotations, ref…

math.NT2025

Class numbers of Imaginary bicyclic biquadratic number fields

Anuj Jakhar, Ravi Kalwaniya, Mahesh Kumar Ram

For any fixed positive integer $n$ , we provide a method to compute all imaginary bicyclic biquadratic number fields with class number $n$ , along with their class group structures,…

math.NT2024★ 1 cited

A Study of monogenity of Binomial Composition

Anuj Jakhar, Ravi Kalwaniya, Prabhakar Yadav

Let $θ$ be a root of a monic polynomial $h (x) \in Z [x]$ of degree $n \geq 2$ . We say $h (x)$ is monogenic if it is irreducible over $\Q$ and ${1, θ, θ^{2}, \dots, θ^{n - 1}}$ is a…

math.NT2023

An extension of a second irreducibility theorem of I. Schur

Anuj Jakhar, Ravi Kalwaniya

Let $n \neq = 8$ be a positive integer such that $n + 1 \neq = 2^{u}$ for any integer $u \geq 2$ . Let $ϕ (x)$ belonging to $Z [x]$ be a monic polynomial which is irreducible modulo a…

math.NT2023★ 1 cited

ON the index divisors of certain number fields

Anuj Jakhar, Ravi Kalwaniya

Let $K=\Q(θ)$ be an algebraic number field with $θ$ a root of an irreducible quadrinomial $f (x) = x^{6} + a x^{m} + b x + c \in Z [x]$ with $m \in {2, 3, 4, 5}$ . In the present paper, we give some…