Metric Diophantine Approximation: the Khintchine–groshev Theorem for Nondegenerate Manifolds
نویسندگان
چکیده
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. 2000 Math. Subj. Class. Primary 11J83; Secondary 11K60.
منابع مشابه
Classical metric Diophantine approximation revisited: the Khintchine-Groshev theorem
Let An,m(ψ) denote the set of ψ-approximable points in R mn. Under the assumption that the approximating function ψ is monotonic, the classical KhintchineGroshev theorem provides an elegant probabilistic criterion for the Lebesgue measure of An,m(ψ). The famous Duffin-Schaeffer counterexample shows that the monotonicity assumption on ψ is absolutely necessary when m = n = 1. On the other hand, ...
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تاریخ انتشار 2002