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

Showing 2023Show all

8 papers · 1 filter

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…

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

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 $x^{7} + a x + b$