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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

An extension of quantitative nondivergence and applications to Diophantine exponents


Author: Dmitry Kleinbock
Journal: Trans. Amer. Math. Soc. 360 (2008), 6497-6523
MSC (2000): Primary 37A17; Secondary 11J83
Published electronically: June 26, 2008
MathSciNet review: 2434296
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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 $ \mathbb{R}^{n}$ and their nondegenerate submanifolds.


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Additional Information

Dmitry Kleinbock
Affiliation: Department of Mathematics, Brandeis University, Waltham, Massachusetts 02454-9110
Email: kleinboc@brandeis.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04592-3
PII: S 0002-9947(08)04592-3
Received by editor(s): December 15, 2006
Published electronically: June 26, 2008
Additional Notes: This work was supported in part by NSF Grant DMS-0239463.
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.