UPPER BOUNDS ON RELATIVE CLASS NUMBERS OF CYCLOTOMIC FIELDS

被引：1
|
作者：
Louboutin, S. [1 ]
机构：
[1] Aix Marseille Univ, Inst Math Luminy, F-13288 Marseille 9, France
来源：
MATHEMATICA SLOVACA | 2014年 / 64卷 / 01期
关键词：
cyclotomic field; class number; relative class number; DIRICHLET-L-FUNCTIONS; EXACT FORMULAS; MEAN-VALUES;
D O I：
10.2478/s12175-013-0183-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
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 root p(p/16)((p-1)/2). (C) 2014 Mathematical Institute Slovak Academy of Sciences
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页码：21 / 26
页数：6
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