Denominators of algebraic numbers in a number field

被引：1

作者：

Ayad, Mohamed ^{[1
]}

Bayad, Abdelmejid ^{[2
]}

Kihel, Omar ^{[3
]}

机构：

[1] Univ Littoral, Lab Math Pures & Appl, F-62228 Calais, France

[2] Univ Evry Val dEssonne, Dept Math, F-91037 Evry, France

[3] Brock Univ, Dept Math, St Catharines, ON L2S 3A1, Canada

来源：

JOURNAL OF NUMBER THEORY | 2015年 / 149卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

Denominators of algebraic numbers; Leading coefficients for algebraic equations; Splitting of prime numbers;

D O I：

10.1016/j.jnt.2014.06.024

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Text. For any algebraic number gamma, let g(x) be the unique irreducible polynomial with integral coefficients, whose leading coefficient c(gamma) is positive, such that g(gamma) = 0. Let d(gamma) be the denominator of gamma. We fix a number field K, a prime p, a positive integer k and we study the set of values of v(p)(c(gamma)), when gamma runs in the set of the primitive elements of K over Q, such that v(p)(d(gamma)) = k. This set is completely determined for certain splitting types of p. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：1 / 14

页数：14