On the Davenport-Heilbronn theorems and second order terms

被引：59

作者：

Bhargava, Manjul ^{[1
]}

Shankar, Arul ^{[2
]}

Tsimerman, Jacob ^{[3
]}

机构：

[1] Princeton Univ, Dept Math, Princeton, NJ 08544 USA

[2] Inst Adv Study, Princeton, NJ 08540 USA

[3] Harvard Univ, Dept Math, Cambridge, MA 02138 USA

来源：

INVENTIONES MATHEMATICAE | 2013年 / 193卷 / 02期

关键词：

CUBIC FIELDS; DENSITY; DISCRIMINANTS; COEFFICIENTS; RINGS;

D O I：

10.1007/s00222-012-0433-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give simple proofs of the Davenport-Heilbronn theorems, which provide the main terms in the asymptotics for the number of cubic fields having bounded discriminant and for the number of 3-torsion elements in the class groups of quadratic fields having bounded discriminant. We also establish second main terms for these theorems, thus proving a conjecture of Roberts. Our arguments provide natural interpretations for the various constants appearing in these theorems in terms of local masses of cubic rings.

引用

页码：439 / 499

页数：61

共 33 条

[1]

[Anonymous], 1941, Progress in Mathematics

[2] On the mean 3-rank of quadratic fields (vol 118, pg 1, 1999) [J].