Integer points close to algebraic curves

被引：0

作者：

Boca, FP

Vâjâitu, M

Zaharescu, A

机构：

[1] Romanian Acad, Inst Math, Bucharest 70700, Romania

[2] Univ Illinois, Dept Math, Urbana, IL 61801 USA

来源：

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES | 2002年 / 65卷

基金：

英国工程与自然科学研究理事会;

关键词：

D O I：

10.1112/S0024610701002812

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For any algebraic curve with unbounded branches in the plane, two numbers in (0,infinity] are defined that measure how closely to the curve it is possible to find infinitely many integer points. These numbers are shown to be 1 for almost all such curves. The state of the art in estimating these numbers for several classes of curves is also discussed.

引用

页码：10 / 26

页数：17

共 16 条

[1]

Baker RC., 1986, DIOPHANTINE INEQUALI

[2] QUANTITATIVE RECURRENCE RESULTS [J].

BOSHERNITZAN, MD .

INVENTIONES MATHEMATICAE, 1993, 113 (03) :617-631

[3]

Elkies ND, 2000, LECT NOTES COMPUT SC, V1838, P33

[4]

Furstenberg H., 1981, RECURRENCE ERGODIC T

[5]

HARMAN G, 1998, London Mathematical Society Monographs. New Series, V18

[6]

KUIPERS L, 1974, UNIFORM DISTRIBUTION

[7] OLD AND NEW CONJECTURED DIOPHANTINE INEQUALITIES [J].

LANG, S .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1990, 23 (01) :37-75

[8]

LeVeque W. J., 1959, J REINE ANGEW MATH, V202, P215

[9]

Roth K. F., 1955, Mathematika, V2, P1

[10]

Schmidt W. M., 1977, REGIONAL C SERIES MA, V32

← 1 2 →