GREENBERG?S CONJECTURE FOR REAL QUADRATIC FIELDS AND THE CYCLOTOMIC Z2-EXTENSIONS

被引：2

作者：

Pagani, Lorenzo ^{[1
]}

机构：

[1] Univ Roma La Sapienza, Dipartimento Matemat, Piazzale Aldo Moro 5, I-00185 Rome, Italy

来源：

MATHEMATICS OF COMPUTATION | 2022年 / 91卷 / 335期

关键词：

INVARIANT; UNITS;

D O I：

10.1090/mcom/3712

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let A(n) be the 2-part of the ideal class group of the n-th layer of the cyclotomic Z(2)-extension of a real quadratic number field F. The cardinality of A(n) is related to the index of cyclotomic units in the full group of units. We present a method to study the latter index. As an application we show that the sequence of the A(n)'s stabilizes for the real fields F = Q(root f) for any integer 0 < f < 10000. Equivalently Greenberg's conjecture holds for those fields.

引用

页码：1437 / 1467

页数：31

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