Counting algebraic integers of fixed degree and bounded height

被引：12

作者：

Barroero, Fabrizio ^{[1
]}

机构：

[1] Graz Univ Technol, Inst Math A, A-8010 Graz, Austria

来源：

MONATSHEFTE FUR MATHEMATIK | 2014年 / 175卷 / 01期

关键词：

Heights; Algebraic integers; Counting; THEOREM;

D O I：

10.1007/s00605-013-0599-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let be a number field. For , we give an asymptotic formula for the number of algebraic integers of absolute Weil height bounded by and fixed degree over .

引用

页码：25 / 41

页数：17

共 16 条

[1] Counting Lattice Points and O-Minimal Structures [J].

Barroero, Fabrizio ;

Widmer, Martin .

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2014, 2014 (18) :4932-4957

[2]

BIERSTONE E, 1988, PUBL MATH-PARIS, P5

[3]

Bombieri E., 2006, HEIGHTS DIOPHANTINE, V4

[4]

Chern SJ, 2001, J REINE ANGEW MATH, V540, P1

[5]

Davenport H., 1951, J. London Math. Soc., Vs1-26, P179

[6]

Gao X, 1995, THESIS U COLORADO CO

[7]

Lang S., 1983, Fundamentals of Diophantine geometry, DOI 10.1007/978-1-4757-1810-2

[8] ON ZEROS OF DERIVATIVE OF A POLYNOMIAL [J].

MAHLER, K .

PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES, 1961, 264 (1317) :145-+

[9] Counting algebraic numbers with large height II [J].

Masser, David ;

Vaaler, Jeffrey D. .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 359 (01) :427-445

[10]

NORTHCOTT DG, 1949, P CAMB PHILOS SOC, V45, P502

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