Diophantine Exponents of Affine Subspaces: The Simultaneous Approximation Case

2008/09/01 by Zhang, Yuqing
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0809.0176

Abstract

We apply nondivergence estimates for flows on homogeneous spaces to compute Diophantine exponents of affine subspaces of \Rⁿ and their nondegenerate submanifolds.

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• An extension of quantitative nondivergence and applications to Diophantine exponents
• Diophantine approximation exponents on homogeneous varieties
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• Diophantine approximation on subspaces of ℝⁿ and dynamics on homogeneous spaces
• Independence of the Diophantine exponents associated with linear subspaces