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On simultaneous diophantine approximations. Vectors of given diophantine type

โœ Scribed by N. G. Moshchevitin

Publisher
SP MAIK Nauka/Interperiodica
Year
1997
Tongue
English
Weight
580 KB
Volume
61
Category
Article
ISSN
0001-4346

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๐Ÿ“œ SIMILAR VOLUMES

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Beginning with an improvement to Dirichlet's Theorem on simultaneous approximation, in this paper we introduce an alogrithm, in sympathy with the classical continued fraction algorithm, to generate the sequence of best approximates to the system max[&: 0 n&, &: 1 n&, ..., &: L n&] in the case when :

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Simultaneous Diophantine Approximation and Asymptotic Formulae on Manifolds
โœ M.M. Dodson; B.P. Rynne; J.A.G. Vickers ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 714 KB

Let (r), r=1, 2, ... be a positive decreasing sequence such that r=1 (r) k diverges. Using a powerful variance argument due to Schmidt, an asymptotic formula is obtained for the number of integer solutions q of the system of Diophantine inequalities max[&qx i &: which holds for almost all points (x