Inhomogeneous theory of dual Diophantine approximation on manifolds

被引：17

作者：

Badziahin, Dzmitry ^{[2
]}

Beresnevich, Victor ^{[1
]}

Velani, Sanju ^{[1
]}

机构：

[1] Univ York, York YO10 5DD, N Yorkshire, England

[2] Univ Durham, Sci Labs, Durham DH1 3LE, England

来源：

ADVANCES IN MATHEMATICS | 2013年 / 232卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

Metric Diophantine approximation; Extremal manifolds; Groshev type theorem; Ubiquitous systems; KHINTCHINE-GROSHEV THEOREM; PLANAR CURVES; HOMOGENEOUS SPACES; RATIONAL-POINTS; CONVERGENCE; FLOWS;

D O I：

10.1016/j.aim.2012.09.022

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The theory of inhomogeneous Diophantine approximation on manifolds is developed. In particular, the notion of nice manifolds is introduced and the divergence part of the Groshev type theory is established for all such manifolds. Our results naturally incorporate and generalize the homogeneous measure and dimension theorems for non-degenerate manifolds established to date. The results have natural applications beyond the standard inhomogeneous theory such as Diophantine approximation by algebraic integers. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：1 / 35

页数：35

共 59 条

[1]

[Anonymous], 1993, GRADUATE TEXTS MATH

[2] A note on simultaneous and multiplicative diophantine approximation on planar curves [J].