Inhomogeneous Diophantine approximation on planar curves
Inhomogeneous Diophantine approximation on planar curves
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DOI：
10.1007/s00208-010-0548-9
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发表时间：
2009-03
影响因子：
1.4
通讯作者：
V. Beresnevich;S. Velani;Robert C. Vaughan
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文献类型：
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作者：
V. Beresnevich;S. Velani;Robert C. Vaughan
本文发展了平面曲线上同时丢番图近似的非齐次度量理论。我们的结果自然地扩展了Beresnevich等人（Ann Math 166(2): 367-426, 2007）和Vaughan和Velani （Invent Math 166:103 - 124, 2006）建立的齐次Khintchine和Jarník类型定理，并且是同类定理中的第一个。关键在于从本质上获得关于平面曲线附近“移位”有理点分布的最佳结果。
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.