Inhomogeneous Diophantine approximation on planar curves

被引：0
|
作者：
V. V. Beresnevich
R. C. Vaughan
S. L. Velani
机构：
[1] University of York,Department of Mathematics
[2] Pennsylvania State University,Department of Mathematics
来源：
Mathematische Annalen | 2011年 / 349卷
关键词：
Primary 11J83; Secondary 11J13; 11K60;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper we develop the inhomogeneous metric theory of simultaneous Diophantine approximation on planar curves. Our results naturally extend the homogeneous Khintchine and Jarník type theorems established in Beresnevich et al. (Ann Math 166(2):367–426, 2007) and Vaughan and Velani (Invent Math 166:103–124, 2006) and are the first of their kind. The key lies in obtaining essentially the best possible results regarding the distribution of ‘shifted’ rational points near planar curves.
引用
收藏
页码：929 / 942
页数：13
相关论文
共 50 条
  • [31] On diophantine approximation along algebraic curves
    Burger, Edward B.
    Pillai, Ashok M.
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 136 (01) : 11 - 19
  • [32] Inhomogeneous Dual Diophantine Approximation on Affine Subspaces
    Beresnevich, Victor
    Ganguly, Arijit
    Ghosh, Anish
    Velani, Sanju
    INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2020, 2020 (12) : 3582 - 3613
  • [33] Hall's ray in inhomogeneous diophantine approximation
    Cusick, TW
    Moran, W
    Pollington, AD
    JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, 1996, 60 : 42 - 50
  • [34] Inhomogeneous theory of dual Diophantine approximation on manifolds
    Badziahin, Dzmitry
    Beresnevich, Victor
    Velani, Sanju
    ADVANCES IN MATHEMATICS, 2013, 232 (01) : 1 - 35
  • [35] METRIC INHOMOGENEOUS DIOPHANTINE APPROXIMATION IN POSITIVE CHARACTERISTIC
    Kristensen, S.
    MATHEMATICA SCANDINAVICA, 2011, 108 (01) : 55 - 76
  • [36] Inhomogeneous Diophantine approximation for generic homogeneous functions
    Kleinbock, Dmitry
    Skenderi, Mishel
    INTERNATIONAL JOURNAL OF NUMBER THEORY, 2023, 19 (06) : 1269 - 1293
  • [37] Inhomogeneous Diophantine approximation with general error functions
    Liao, Lingmin
    Rams, Michal
    ACTA ARITHMETICA, 2013, 160 (01) : 25 - 35
  • [38] Inhomogeneous diophantine approximation of some Hurwitzian numbers
    Bumby, Richard T.
    Flahive, Mary E.
    DIOPHANTINE ANALYSIS AND RELATED FIELDS - DARF 2007/2008, 2008, 976 : 31 - +
  • [39] On inhomogeneous diophantine approximation and the Borweins' algorithm, II
    Komatsu, T
    ANALYTIC NUMBER THEORY, 2002, 6 : 223 - 242
  • [40] On inhomogeneous Diophantine approximation and the NST-algorithm
    Komatsu, T
    NUMBER THEORY AND ITS APPLICATIONS, 1999, 2 : 241 - 251
12345