A GENERALIZATION OF JAKUBEC'S FORMULA RELATED TO THE MULTIPLICATION THEOREM FOR BERNOULLI POLYNOMIALS

被引：0

作者：

Hirabayashi, Mikihito ^{[1
,2
]}

机构：

[1] Kanazawa Inst Technol, 7-1 Ohgigaoka, Nonoichi, Ishikawa 9218501, Japan

[2] 1-21-4 Ekinishishinmachi, Kanazawa, Ishikawa 9200027, Japan

来源：

JP JOURNAL OF ALGEBRA NUMBER THEORY AND APPLICATIONS | 2021年 / 51卷 / 01期

关键词：

relative class number; imaginary abelian number field; cyclotomic field; determinant;

D O I：

10.17654/NT051010001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In 2017, Jakubec gave a formula for the relative class number of the pth cyclotomic field, p an odd prime, by using a determinant related to the multiplication theorem for Bernoulli polynomials. We generalize his formula to an imaginary abelian number field and also determine the sign of the formula, which he had not given. As a corollary, we also determine the sign in a formula of Carlitz and Olson.

引用

页码：1 / 26

页数：26

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