ON SIMULTANEOUS RATIONAL APPROXIMATION TO A p-ADIC NUMBER AND ITS INTEGRAL POWERS

被引:10
作者
Bugeaud, Yann [1 ]
Budarina, Natalia [2 ]
Dickinson, Detta [2 ]
O'Donnell, Hugh [2 ]
机构
[1] Univ Strasbourg, UFR Math & Informat, F-67084 Strasbourg, France
[2] Natl Univ Maynooth, Dept Math, Maynooth, Kildare, Ireland
基金
爱尔兰科学基金会;
关键词
Diophantine approximation; Hausdorff dimension; p-adic number; DIOPHANTINE APPROXIMATION; PLANAR CURVES; EXPONENTS;
D O I
10.1017/S001309151000060X
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let p be a prime number. For a positive integer n and a p-adic number xi, let lambda(n) (xi) denote the supremum of the real numbers lambda such that there are arbitrarily large positive integers q such that parallel to q xi parallel to(p), parallel to q xi(2)parallel to(p), ... , parallel to q xi(n)parallel to(p) are all less than q(-lambda-1). Here, parallel to x parallel to(p) denotes the infimum of vertical bar x-n vertical bar(p) as n runs through the integers. We study the set of values taken by the function lambda(n).
引用
收藏
页码:599 / 612
页数:14
相关论文
共 16 条
[1]  
BERESNEVICH V, 2006, MEMOIRS AM MATH SOC, V846
[2]   Diophantine approximation on planar curves and the distribution of rational points [J].
Beresnevich, Victor ;
Dickinson, Detta ;
Velani, Sanju ;
Vaughan, R. C. .
ANNALS OF MATHEMATICS, 2007, 166 (02) :367-426
[3]  
Bernik V. I., 1999, Cambridge Tracts in Mathematics, V137
[4]   SIMULTANEOUS DIOPHANTINE APPROXIMATION ON POLYNOMIAL CURVES [J].
Budarina, Natalia ;
Dickinson, Detta ;
Levesley, Jason .
MATHEMATIKA, 2010, 56 (01) :77-85
[5]   Exponents of diophantine approximation and Sturmian continued fractions [J].
Bugeaud, Y ;
Laurent, M .
ANNALES DE L INSTITUT FOURIER, 2005, 55 (03) :773-+
[6]  
Bugeaud Y., 2004, CAMBRIDGE TRACTS MAT, V160
[7]  
Bugeaud Y, 2007, CRM SER, V4, P101
[8]   ON SIMULTANEOUS RATIONAL APPROXIMATION TO A REAL NUMBER AND ITS INTEGRAL POWERS [J].
Bugeaud, Yann .
ANNALES DE L INSTITUT FOURIER, 2010, 60 (06) :2165-2182
[9]  
GUTING R, 1968, J REINE ANGEW MATH, V232, P122
[10]  
Mahler K., 1939, Mat. Fys, V68, P85