On the exceptional sets in Sylvester continued fraction expansion
2015 ◽
Vol 11
(08)
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pp. 2369-2380
Keyword(s):
In this paper, we study some exceptional sets of points whose partial quotients in their Sylvester continued fraction expansions obey some restrictions. More precisely, for α ≥ 1 we prove that the Hausdorff dimension of the set [Formula: see text] is one. In addition, we find that the points whose partial quotients in their Sylvester continued fraction expansions obey some property of divisibility have the same Engel continued fraction expansion and Sylvester continued fraction expansion. And we establish that the set of points whose Engel continued fraction expansion and Sylvester continued fraction expansion coincide is uncountable.
2009 ◽
Vol 29
(5)
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pp. 1451-1478
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2009 ◽
Vol 146
(1)
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pp. 207-212
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2016 ◽
Vol 164
(1)
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pp. 1-14
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Vol 09
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pp. 1237-1247
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2015 ◽
Vol 160
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pp. 401-412
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2020 ◽
Vol 102
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pp. 196-206
2004 ◽
Vol 143
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pp. 285-298
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