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