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pro vyhledávání: '"Jakhar, Anuj"'
Let $\theta$ 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 $\{ 1, \theta, \theta^2, \ldots, \theta^{n-1} \}$ is a basis for the ring $\Z_K$ of integers of $K = \Q(
Externí odkaz:
http://arxiv.org/abs/2402.10131
Let $m\geq 1$ and $a_m$ be integers. Let $\alpha$ be a rational number which is not a negative integer such that $\alpha = \frac{u}{v}$ with $\gcd(u,v) = 1, v>0$. Let $\phi(x)$ belonging to $\Z[x]$ be a monic polynomial which is irreducible modulo al
Externí odkaz:
http://arxiv.org/abs/2306.06890
Autor:
Jakhar, Anuj
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 $2n+1 \neq 3^u$ for any integer $u\geq 2$ according as $c = 0$ or not. Let $\phi(x)$ belonging to $\mathbb{Z}[x]$ be a monic polynomial
Externí odkaz:
http://arxiv.org/abs/2306.01767
Autor:
Jakhar, Anuj, Kalwaniya, Ravi
Let $n \neq 8$ be a positive integer such that $n+1 \neq 2^u$ for any integer $u\geq 2$. Let $\phi(x)$ belonging to $\mathbb{Z}[x]$ be a monic polynomial which is irreducible modulo all primes less than or equal to $n+1$. Let $a_j(x)$ with $0\leq j\l
Externí odkaz:
http://arxiv.org/abs/2306.03294
Autor:
Jakhar, Anuj, Kumar, Surender
Suppose $m$ be a $12$-th power free integer. Let $K=\mathbb{Q}(\theta)$ be an algebraic number field defined by a complex root $\theta$ of an irreducible polynomial $x^{12}-m$ and $O_K$ be its ring of integers. In this paper, we determine the highest
Externí odkaz:
http://arxiv.org/abs/2304.00339
Autor:
Jakhar, Anuj, Kotyada, Srinivas
Let $n$ be a positive integer and $f_n(x)= 1+x+\frac{x^2}{2!}+\cdots + \frac{x^n}{n!}$ denote the $n$-th Taylor polynomial of the exponential function. Let $K = \mathbf{Q}(\theta)$ be an algebraic number field where $\theta$ is a root of $f_n(x)$ and
Externí odkaz:
http://arxiv.org/abs/2303.08100
Let $f(x)=x^n+ax^2+bx+c \in \Z[x]$ be an irreducible polynomial with $b^2=4ac$ and let $K=\Q(\theta)$ be an algebraic number field defined by a complex root $\theta$ of $f(x)$. Let $\Z_K$ deonote the ring of algebraic integers of $K$. The aim of this
Externí odkaz:
http://arxiv.org/abs/2303.03138
Autor:
Jakhar, Anuj, Kalwaniya, Ravi
Let $K=\Q(\theta)$ be an algebraic number field with $\theta$ a root of an irreducible quadrinomial $f(x) = x^6+ax^m+bx+c\in\Z[x] $ with $m\in\{2,3,4,5\}$. In the present paper, we give some explicit conditions involving only $a,~b,~c$ and $m$ for wh
Externí odkaz:
http://arxiv.org/abs/2303.00484
Let $f(x)=x^7+ax+b$ be an irreducible polynomial having integer coefficients and $K=\mathbb{Q}(\theta)$ be an algebraic number field generated by a root $\theta$ of $f(x)$. In the present paper, for every rational prime $p$, our objective is to deter
Externí odkaz:
http://arxiv.org/abs/2301.00365