Lower bounds for the least prime in Chebotarev

被引：3
|
作者：
Fiori, Andrew [1 ]
机构：
[1] Univ Lethbridge, Dept Math & Comp Sci, Lethbridge, AB, Canada
来源：
ALGEBRA & NUMBER THEORY | 2019年 / 13卷 / 09期
关键词：
Chebotarev; class groups; IDEAL;
D O I：
10.2140/ant.2019.13.2199
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we show there exists an infinite family of number fields L, Galois over Q, for which the smallest prime p of Q which splits completely in L has size at least (log(vertical bar D-L vertical bar))(2+o(1)). This gives a converse to various upper bounds, which shows that they are best possible.
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页码：2199 / 2203
页数：5
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