PRIME NUMBERS IN CERTAIN ARITHMETIC PROGRESSIONS

被引：0

作者：

Murty, M. Ram ^{[1
]}

Thain, Nithum ^{[1
]}

机构：

[1] Queens Univ, Dept Math, Jeffery Hall,99 Univ Ave, Kingston, ON K7L 3N6, Canada

来源：

FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI | 2006年 / 35卷 / 01期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Dirichlet's theorem; prime divisors of polynomials; Chebotarev density theorem;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We discuss to what extent Euclid's elementary proof of the infinitude of primes can be modified so as to show infinitude of primes in arithmetic progressions (Dirichlet's theorem). Murty had shown earlier that such proofs can exist if and only if the residue class (mod k) has order 1 or 2. After reviewing this work, we consider generalizations of this question to algebraic number fields.

引用

页码：249 / 259

页数：11

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