Khintchine's singular Diophantine systems and their applications

N. G. Moshchevitin

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 65 (2010) no. 3, pp. 433-511

Résumé

This paper is a survey of classical and recent methods in Diophantine approximation theory and its applications related to Khintchine's results on the existence of real numbers admitting extremely good approximations by rational numbers. Bibliography: 145 titles.

Détail

Keywords: Khintchine's singular systems, continued fractions, best approximations, Diophantine inequalities, transference theorems, Kozlov problem, Peres–Schlag method.
Mots-clés : multidimensional Diophantine approximations

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