Upper bounds on relative class numbers of cyclotomic fields

Mathematica Slovaca

S. Louboutin¹ 

关键词: cyclotomic field;    class number;    relative class number;   

DOI  :  10.2478/s12175-013-0183-5

学科分类：数学（综合）

来源: Slovenska Akademia Vied * Matematicky Ustav / Slovak Academy of Sciences, Mathematical Institute

【 摘 要 】

We explain how one can use the explicit formulas for the mean square values of L-functions which we established elsewhere to obtain explcit upper bounds on relative class numbers of cyclotomic number fields. As an example, we show that the relative class numbers of the cyclotomic fields of conductor 4p, p ≥ 3 a prime, are less than or equal to 8√p(p/16)(p−1)/2.

【 授权许可】

Unknown