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- W2055365819 abstract "Let x [0, 1) and [a1(x), a2(x), ...] be the continued fraction expansion of x. For any n ? 1, write . Khintchine (1935 Compos. Math. 1 361?82) proved that converges in measure to with respect to , where denotes the one dimensional Lebesgue measure. Philipp (1988 Monatsh. Math. 105 195?206) showed that there is not a reasonable normalizing sequence such that a strong law of large numbers is satisfied. In this paper, we show that for any ? ? 0, the set is of Hausdorff dimension 1. Furthermore, we prove that the Hausdorff dimension of the set consisting of reals whose sums of partial quotients grow at a given polynomial rate is 1." @default.
- W2055365819 created "2016-06-24" @default.
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- W2055365819 date "2011-03-03" @default.
- W2055365819 modified "2023-09-26" @default.
- W2055365819 title "On the distribution for sums of partial quotients in continued fraction expansions" @default.
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- W2055365819 doi "https://doi.org/10.1088/0951-7715/24/4/009" @default.
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