Zobrazeno 1 - 10
of 171
pro vyhledávání: '"11r21"'
Let $K$ be a number field with ring of integers $\mathcal{O}_K$, and let $f(x)\in\mathcal{O}_K[x]$ be a monic, irreducible polynomial. We establish necessary and sufficient conditions in terms of the critical points of $f(x)$ for the iterates of $f(x
Externí odkaz:
http://arxiv.org/abs/2412.10358
Autor:
Das, Jishu
Let $F$ be a multi-quadratic totally real number field. Let $\sigma_1,\dots, \sigma_r$ denote its distinct embeddings. Given $s \in F,$ we give an explicit formula for $\| \sigma(s)\|$ and $\sum_{i
Externí odkaz:
http://arxiv.org/abs/2411.02575
Autor:
Smith, Hanson
We explicitly describe the splitting of odd integral primes in the radical extension $\mathbb{Q}(\sqrt[n]{a})$, where $x^n-a$ is an irreducible polynomial in $\mathbb{Z}[x]$. Our motivation is to classify common index divisors, the primes whose split
Externí odkaz:
http://arxiv.org/abs/2409.08911
Autor:
Chatterjee, Tapas, Kumar, Karishan
Let $\theta$ be an algebraic integer and $f(x)=x^{n}+ax^{n-1}+bx+c$ be the minimal polynomial of $\theta$ over the rationals. Let $K=\mathbb{Q}(\theta)$ be a number field and $\mathcal{O}_{K}$ be the ring of integers of $K.$ In this article, we chara
Externí odkaz:
http://arxiv.org/abs/2408.14524
Autor:
Chatterjee, Tapas, Kumar, Karishan
Let $f(x)=x^{n}+ax^{3}+bx+c$ be the minimal polynomial of an algebraic integer $\theta$ over the rationals with certain conditions on $a,~b,~c,$ and $n.$ Let $K=\mathbb{Q}(\theta)$ be a number field and $\mathcal{O}_{K}$ be the ring of integers of $K
Externí odkaz:
http://arxiv.org/abs/2408.14117
Autor:
Maarefparvar, Abbas
We prove two conjectures proposed by Chabert and Halberstadt concerning P\'olya groups of $S_4$-fields and $D_4$-fields. More generally, the latter will be proved for $D_n$-fields with $n \geq 4$ an even integer. Further, generalizing a result of Zan
Externí odkaz:
http://arxiv.org/abs/2408.09019
Morton and Vivaldi defined the polynomials whose roots are parabolic parameters for a one-parameter family of polynomial maps. We call these polynomials delta factors. They conjectured that delta factors are irreducible for the family $z\mapsto z^2+c
Externí odkaz:
http://arxiv.org/abs/2408.04850
Autor:
Yakkou, Hamid Ben, Boudine, Brahim
Let $m$ be a rational integer $(m \neq 0, \pm 1)$ and consider a pure number field $K = \mathbb{Q} (\sqrt[n]{m}) $ with $n \ge 3$. Most papers discussing the monogenity of pure number fields focus only on the case where $m$ is square-free. In this pa
Externí odkaz:
http://arxiv.org/abs/2407.00819
Autor:
Smith, Hanson, Wolske, Zack
We investigate monogenicity and prime splitting in extensions generated by roots of iterated quadratic polynomials. Let $f(x)\in\mathbb{Z}[x]$ be an irreducible, monic, quadratic polynomial, and write $f^n(x)$ for the $n^{\text{th}}$ iterate. We obta
Externí odkaz:
http://arxiv.org/abs/2406.03629
Autor:
Hori, Haruto, Kida, Masanari
In their recent paper, Rosen, Takeyama, Tasaka, and Yamamoto constructed recurrent sequences providing a decomposition law of primes in a Galois extension. In this paper, we reconstruct their sequences via representation theory of finite groups and o
Externí odkaz:
http://arxiv.org/abs/2402.16357