Counting algebraic points of bounded height on projective spaces

被引：5

作者：

Guignard, Quentin

机构：

来源：

JOURNAL OF NUMBER THEORY | 2017年 / 170卷

关键词：

Heights; Algebraic points; Height zeta functions;

D O I：

10.1016/j.jnt.2016.06.008

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove new estimates on the number of algebraic points of fixed degree and bounded height on projective spaces over a given number field. These results extend previous works of Wolfgang Schmidt [13], Gao Xia [3] and Martin Widmer [18]. Our approach, based on zeta functions, also gives a new proof of Schanuel's theorem. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：103 / 141

页数：39

共 18 条

[1] ON SIEGEL LEMMA [J].

BOMBIERI, E ;

VAALER, J .

INVENTIONES MATHEMATICAE, 1983, 73 (01) :11-32

[2]

DATSKOVSKY B, 1988, J REINE ANGEW MATH, V386, P116

[3]

Gao X., 1985, THESIS

[4] Slopes of adelic vectorial bundles over global fields [J].

Gaudron, Eric .

RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA, 2008, 119 :21-95

[5]

Grayson D., 1984, COMMENT MATH HELV, P59

[6]

Groenewegen R.P., 2001, J THEOR NOMBRES BORD, V13

[7]

LANG S, 1970, ALGEBRAIC NUMBER THE

[8]

Le Rudulier C., 2014, J THEOR NOMBRES BORD, V26

[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] ORDERS OF QUADRATIC EXTENSIONS OF NUMBER-FIELDS [J].

NAKAGAWA, J .

ACTA ARITHMETICA, 1994, 67 (03) :229-239

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