A NOTE ON THE RELATIVE GROWTH RATE OF THE MAXIMAL DIGITS IN LÜROTH EXPANSIONS
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This paper is concerned with the growth rate of the maximal digits relative to the rate of approximation of the number by its convergents, as well as relative to the rate of the sum of digits for the Lüroth expansion of an irrational number. The Hausdorff dimension of the sets of points with a given relative growth rate is proved to be full.
2002 ◽
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