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Moscow Mathematical Journal, 2002, Volume 2, Number 2, Pages 203–225
DOI: https://doi.org/10.17323/1609-4514-2002-2-2-203-225 (Mi mmj53) 		 
This article is cited in 66 scientific papers (total in 66 papers)

Metric Diophantine Approximation: The Khintchine–Groshev Theorem for Nondegenerate Manifolds

V. V. Beresnevicha, V. I. Bernika, D. Ya. Kleinbockb, G. A. Margulisc

a Institute of Mathematics, National Academy of Sciences of the Republic of Belarus
b Brandeis University
c Yale University
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DOI: https://doi.org/10.17323/1609-4514-2002-2-2-203-225
Abstract: The main objective of this paper is to prove a Khintchine type theorem on divergence of linear Diophantine approximation on nondegenerate manifolds, which completes earlier results for convergence.
Key words and phrases: Diophantine approximation, Khintchine type theorems, metric theory of Diophantine approximation.
Received: January 30, 2002; in revised form April 11, 2002
Bibliographic databases:
MSC: Primary 11J83; Secondary 11K60
Language: English
Citation: V. V. Beresnevich, V. I. Bernik, D. Ya. Kleinbock, G. A. Margulis, “Metric Diophantine Approximation: The Khintchine–Groshev Theorem for Nondegenerate Manifolds”, Mosc. Math. J., 2:2 (2002), 203–225
Citation in format AMSBIB
\Bibitem{BerBerKle02}
\by V.~V.~Beresnevich, V.~I.~Bernik, D.~Ya.~Kleinbock, G.~A.~Margulis
\paper Metric Diophantine Approximation: The Khintchine--Groshev Theorem for Nondegenerate Manifolds
\jour Mosc. Math.~J.
\yr 2002
\vol 2
\issue 2
\pages 203--225
\mathnet{http://mi.mathnet.ru/mmj53}
\crossref{https://doi.org/10.17323/1609-4514-2002-2-2-203-225}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1944505}
\zmath{https://zbmath.org/?q=an:1013.11039}
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