NOTE ON THE CLASS NUMBER OF IMAGINARY QUADRATIC NUMBER FIELDS AND SOPHIE GERMAIN PRIMES

被引：0

作者：

Li, Anly ^{[1
]}

机构：

[1] Fu Jen Catholic Univ, Dept Math, Taipei, Taiwan

来源：

JP JOURNAL OF ALGEBRA NUMBER THEORY AND APPLICATIONS | 2023年 / 62卷 / 02期

关键词：

class number; Sophie Germain prime;

D O I：

10.17654/0972555523027

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let p > 2 be a Sophie Germain prime which means that q = 2 p +1 is also a prime. Let K = Q( root -q) and denote its ideal class number by h(K). We use Kummer congruences and Bernoulli numbers to study the relation between p and h(K). We prove that -h(K) equivalent to k & sdot;p (mod q) for some positive integer k.

引用

页码：159 / 165

页数：7