ON THE FAST INCREASING DIGITS IN LÃœROTH EXPANSIONS

LÜ Meiying and Jing Xie ()
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LÜ Meiying: School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, P. R. China
Jing Xie: School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, P. R. China

FRACTALS (fractals), 2021, vol. 29, issue 07, 1-7

Abstract: For any x ∈ (0, 1], let x = 1 d1 + 1 d1(d1 − 1)d2 + ⋯ + 1 d1(d1 − 1)⋯dn−1(dn−1 − 1)dn + ⋯ be its Lüroth expansion with digits {dj ≥ 2,j ≥ 1}. Let ψ : ℕ → ℠+ be a function satisfying ψ(n)/n →∞ as n →∞ and E(ψ) := x ∈ (0, 1] :limn→∞ 1 ψ(n)∑j=1nlog d j(x) = 1 . In this paper, we give the Hausdorff dimension of the set E(ψ) without any extra condition on ψ. This result extends the former work of the first author (Fractals 28(4) (2020) 2050064, doi:10.1142/S0218348X20500644).

Keywords: Lüroth Expansions; Exceptional Sets; Hausdorff Dimensions (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21502200

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