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., 2002, Volume 2, Number 2,Pages <nobr>203

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

V. V. Beresnevich^a, V. I. Bernik^a, D. Ya. Kleinbock^b, G. A. Margulis^c

^a Institute of Mathematics, National Academy of Sciences of the Republic of Belarus
^b Brandeis University
^c Yale University

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.

MSC: Primary 11J83; Secondary 11K60

Received: January 30, 2002; in revised form April 11, 2002

Language: English

DOI: 10.17323/1609-4514-2002-2-2-203-225