A. Jakhar

activity

20162026

most citedOn the irreducible factors of a polynomial II

5 citations · 10 across the 22 of their papers we have counts for

collaborators

25 papers

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

A primality test for $K p^{ℓ} - 1$ numbers

Anuj Jakhar, Mahesh Kumar Ram

We develop an algebraic framework over arbitrary quadratic fields $L = Q (D)$ to generalize the Miller-Rabin primality test. Consequently, we present a deterministic…

math.NT2026

On the distribution of shapes of totally real multiquadratic number fields

Anuj Jakhar, Anwesh Ray

The shape of a number field $K$ of degree $m$ is defined as the equivalence class of the lattice of integers under linear operations generated by rotations, reflections, and positi…

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 octic Kummer extensions

Anuj Jakhar, Anwesh Ray

The shape of a number field $K$ of degree $n$ is defined as the equivalence class of the lattice of integers under linear operations generated by rotations, reflections, and positi…

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.NT2025

Behaviour of Newton Polygon over polynomial composition

Anuj Jakhar, Shanta Laishram, Kotyada Srinivas +1

In this paper, we study the structure of Newton polygons for compositions of polynomials over the rationals. We establish sufficient conditions under which the successive vertices…

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

On the irreducibility of extended Laguerre Polynomials

Anuj Jakhar, Srinivas Kotyada, Arunabha Mukhopadhyay

Let $m \geq 1$ and $a_{m}$ be integers. Let $α$ be a rational number which is not a negative integer such that $α = \frac{u}{v}$ with $g cd (u, v) = 1, v > 0$ . Let $ϕ (x)$ belonging to $\Z[…

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 Schur's irreducibility results and generalised $ϕ$ -Hermite polynomials

Anuj Jakhar

Let $c$ be a fixed integer such that $c \in {0, 2} .$ Let $n$ be a positive integer such that either $n \geq 2$ or $2 n + 1 \neq = 3^{u}$ for any integer $u \geq 2$ according as $c = 0$ or…

math.NT2023

DISCRIMINANT and integral basis OF $Q (12 a)$

Anuj Jakhar, Surender Kumar

Suppose $m$ be a $12$ -th power free integer. Let $K = Q (θ)$ be an algebraic number field defined by a complex root $θ$ of an irreducible polynomial $x^{12} - m$ and $O_{K}$ be i…

math.NT2023

On power basis of a class of number fields

Anuj Jakhar, Sumandeep Kaur, Surender Kumar

Let $f (x) = x^{n} + a x^{2} + b x + c \in Z [x]$ be an irreducible polynomial with $b^{2} = 4 a c$ and let $K=\Q(θ)$ be an algebraic number field defined by a complex root $θ$ of $f (x)$ . Let $Z_{K}$ de…

math.NT2023

A short note on number fields defined by exponential Taylor polynomials

Anuj Jakhar, Srinivas Kotyada

Let $n$ be a positive integer and $f_{n} (x) = 1 + x + \frac{x ^{2}}{2 !} + \dots + \frac{x ^{n}}{n !}$ denote the $n$ -th Taylor polynomial of the exponential function. Let $K = Q (θ)$ be 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…

math.NT2023★ 1 cited

On common index divisor of the number fields defined by $x^{7} + a x + b$

Anuj Jakhar, Sumandeep Kaur, Surender Kumar

Let $f (x) = x^{7} + a x + b$ be an irreducible polynomial having integer coefficients and $K = Q (θ)$ be an algebraic number field generated by a root $θ$ of $f (x)$ . In the present pa…

math.NT2022

Discriminant and integral basis of pure nonic fields

Anuj Jakhar, Neeraj Sangwan

Let $K = \Q(θ)$ be an algebraic number field with $θ$ satisfying an irreducible polynomial $x^{9} - a$ over the field $\Q$ of rationals and $Z_{K}$ denote the ring of algebraic inte…

math.NT2020

On integral basis of pure number fields

Anuj Jakhar, Sudesh K. Khanduja, Neeraj Sangwan

Let $K = Q (n a)$ be an extension of degree $n$ of the field $\Q$ of rational numbers, where the integer $a$ is such that for each prime $p$ dividing $n$ either $p\nm…

math.NT2020

On the discriminant of pure number fields

Anuj Jakhar, Sudesh K. Khanduja, Neeraj Sangwan

Let $K = Q (n a)$ be an extension of degree $n$ of the field $\Q$ of rational numbers, where the integer $a$ is such that for each prime $p$ dividing $n$ either $p\nm…

math.NT2020★ 5 cited

On the irreducible factors of a polynomial II

Anuj Jakhar, Srinivas Koytada

We give a lower bound for the degree of an irreducible factor of a given polynomial. This improves and generalizes the results obtained in [4, On the irreducible factors of a polyn…

math.AC2016★ 1 cited

An irreducibility criterion for integer polynomials

Anuj Jakhar, Neeraj Sangwan

Let $f (x) = i = 0 \sum n a_{i} x^{i}$ be a polynomial with coefficients from the ring $Z$ of integers satisfying either $(i)$ $0 < a_0 \leq a_{1} \leq \cdots \leq a…

On The Index of Polynomial Compositions over Valued Fields

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

Monogenic Fields from Polynomial Compositions with Applications

A primality test for Kpℓ−1 numbers

On the distribution of shapes of totally real multiquadratic number fields

Arithmetic Aspects of Number Fields Generated by Polynomial Families

On the distribution of shapes of octic Kummer extensions

On the distribution of shapes of sextic pure number fields

Class numbers of Imaginary bicyclic biquadratic number fields

Behaviour of Newton Polygon over polynomial composition

A Study of monogenity of Binomial Composition

On the irreducibility of extended Laguerre Polynomials

An extension of a second irreducibility theorem of I. Schur

On Schur's irreducibility results and generalised ϕ-Hermite polynomials

DISCRIMINANT and integral basis OF Q(12a​)

On power basis of a class of number fields

A short note on number fields defined by exponential Taylor polynomials

ON the index divisors of certain number fields

On common index divisor of the number fields defined by x7+ax+b

Discriminant and integral basis of pure nonic fields

On integral basis of pure number fields

On the discriminant of pure number fields

On the irreducible factors of a polynomial II

An irreducibility criterion for integer polynomials

A primality test for $K p^{ℓ} - 1$ numbers

On Schur's irreducibility results and generalised $ϕ$ -Hermite polynomials

DISCRIMINANT and integral basis OF $Q (12 a)$

On common index divisor of the number fields defined by $x^{7} + a x + b$