Cohen-Lenstra heuristics and the Spiegelungssatz; function fields

被引：5

作者：

Lee, YJ ^{[1
]}

机构：

[1] Smith Coll, Dept Math, Clark Sci Ctr, Northampton, MA 01063 USA

来源：

JOURNAL OF NUMBER THEORY | 2004年 / 106卷 / 02期

关键词：

class groups; Cohen-Lenstra heuristics; Spiegelungssatz; cyclic function field;

D O I：

10.1016/j.jnt.2004.01.001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the compatibility of Cohen-Lenstra heuristics with Leopoldt's Spiegelungssatz (= the reflection theorem) in the case of cyclic function fields. First, we prove a group-theoretical version of the Spiegelungssatz for cyclic function fields. Then we show the internal consistency of the function field analogue of Cohen-Lenstra heuristics in the case of cyclic function fields. It thus supports the validity of Cohen-Lenstra heuristics in function fields. (C) 2004 Elsevier Inc. All rights reserved.

引用

页码：187 / 199

页数：13

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