Weakly divergent partial quotients
2019 ◽
Vol 13
(01)
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pp. 2050158
Keyword(s):
We study the real numbers with partial quotients diverging to infinity in a subsequence. We show that if the subsequence has positive density then such sets have Hausdorff dimension equal to 1/2. This generalizes one of the results obtained in [C. Y. Cao, B. W. Wang and J. Wu, The growth speed of digits in infinite iterated function systems, Studia. Math. 217(2) (2013) 139–158; I. J. Good, The fractional dimensional theory of continued fractions, Proc. Cambridge Philos. Soc. 37 (1941) 199–228].
2011 ◽
Vol 139
(08)
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pp. 2767-2767
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2010 ◽
Vol 149
(1)
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pp. 147-172
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2016 ◽
Vol 102
(3)
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pp. 435-443
2019 ◽
Vol 150
(1)
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pp. 261-275
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2014 ◽
Vol 10
(04)
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pp. 849-857
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2002 ◽
Vol 181
(2)
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pp. 223-237
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Keyword(s):