发布求助
文献互助 智能选刊 最新文献

Infinite Parametric Families of Irreducible Polynomials with a Prescribed Number of Complex Roots

离散数学期刊(英文) Pub Date : 2019-01-01 DOI:10.4236/ojdm.2019.91001
Catalin Nitica, V. Nitica
{"title":"Infinite Parametric Families of Irreducible Polynomials with a Prescribed Number of Complex Roots","authors":"Catalin Nitica, V. Nitica","doi":"10.4236/ojdm.2019.91001","DOIUrl":null,"url":null,"abstract":"In this note, for any pair of natural numbers (n,k), n≥3, k≥1, and 2k<n, we construct an infinite family of irreducible polynomials of degree n, with integer coefficients, that has exactly n-2k complex non-real roots if n is even and has exactly n-2k-1 complex non-real roots if n is odd. Our work generalizes a technical result of R. Bauer, presented in the classical monograph “Basic Algebra” of N. Jacobson. It is used there to construct polynomials with Galois groups, the symmetric group. Bauer’s result covers the case k=1 and n odd prime.","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"离散数学期刊(英文)","FirstCategoryId":"1093","ListUrlMain":"https://doi.org/10.4236/ojdm.2019.91001","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

Abstract

In this note, for any pair of natural numbers (n,k), n≥3, k≥1, and 2k
分享
查看原文 本刊更多论文
具有一定复根数的不可约多项式的无限参数族
对于任意一对自然数(n,k)， n≥3,k≥1,2k
本文章由计算机程序翻译，如有差异，请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
离散数学期刊(英文)
离散数学期刊(英文)
自引率
0.00%
发文量
127
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信