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An extension of quantitative nondivergence and applications to Diophantine exponents

Dmitry Kleinbock
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Abstract

We present a sharpening of nondivergence estimates for unipotent (or more generally polynomial-like) flows on homogeneous spaces. Applied to metric Diophantine approximation, it yields precise formulas for Diophantine exponents of affine subspaces of $\Bbb R^n$ and their nondegenerate submanifolds.

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Dmitry Kleinbock. 2008-05-19. An extension of quantitative nondivergence and applications to Diophantine exponents. https://arxiv.org/abs/math/0508517

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