Distribution of orders in number fields

被引：9

作者：

Kaplan, Nathan ^{[1
]}

Marcinek, Jake ^{[2
]}

Takloo-Bighash, Ramin ^{[3
]}

机构：

[1] Yale Univ, Dept Math, New Haven, CT 06520 USA

[2] CALTECH, Dept Math, Pasadena, CA 91125 USA

[3] Univ Illinois, Dept Math Stat & Comp Sci, 851 S Morgan St,M-C 249, Chicago, IL 60607 USA

来源：

RESEARCH IN THE MATHEMATICAL SCIENCES | 2015年 / 2卷 / 01期

基金：

美国国家科学基金会;

关键词：

Orders; p-adic and motivic integration; Subring zeta function;

D O I：

10.1186/s40687-015-0027-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the distribution of orders of bounded discriminants in number fields. We use the zeta functions introduced by Grunewald, Segal, and Smith. In order to carry out our study, we use p-adic and motivic integration techniques to analyze the zeta function. We give an asymptotic formula for the number of orders contained in the ring of integers of a quintic number field. We also obtain non-trivial bounds for higher degree number fields.

引用

页数：57

共 27 条

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[Anonymous], 1955, THEORY GROUPS FINITE

[2]

[Anonymous], 1967, Endliche Gruppen I, Die Grundlehren der Mathematischen Wissenschaften

[3]

[Anonymous], 1986, GRUNDLEHREN MATH WIS

[4]

Bhargava M, 2008, ANN MATH, V167, P53

[5] The density of discriminants of quintic rings and fields [J].