Exceptional sets related to the largest digits in Lüroth expansions
Keyword(s):
Let [Formula: see text] denote the largest digit of the first [Formula: see text] terms in the Lüroth expansion of [Formula: see text]. Shen, Yu and Zhou, A note on the largest digits in Luroth expansion, Int. J. Number Theory 10 (2014) 1015–1023 considered the level sets [Formula: see text] and proved that each [Formula: see text] has full Hausdorff dimension. In this paper, we investigate the Hausdorff dimension of the following refined exceptional set: [Formula: see text] and show that [Formula: see text] has full Hausdorff dimension for each pair [Formula: see text] with [Formula: see text]. Combining the two results, [Formula: see text] can be decomposed into the disjoint union of uncountably many sets with full Hausdorff dimension.
2010 ◽
Vol 149
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pp. 147-172
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Keyword(s):
2017 ◽
Vol 13
(10)
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pp. 2777-2790
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2016 ◽
Vol 94
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pp. 15-19
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2018 ◽
Vol 458
(1)
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pp. 464-480