The number of extensions of a number field with fixed degree and bounded discriminant

被引：59

作者：

Ellenberg, Jordan S. ^{[1
]}

Venkatesh, Akshay

机构：

[1] Univ Wisconsin, Madison, WI 53706 USA

[2] NYU, Courant Inst Math Sci, New York, NY USA

来源：

ANNALS OF MATHEMATICS | 2006年 / 163卷 / 02期

关键词：

D O I：

10.4007/annals.2006.163.723

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give an upper bound on the number of extensions of a fixed number field of prescribed degree and discriminant <= X; these bounds improve on work of Schmidt. We also prove various related results, such as lower bounds for the number of extensions and upper bounds for Galois extensions.

引用

页码：723 / 741

页数：19

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