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- Title
SOME RESULTS ON THE LARGEST PARTIAL QUOTIENT IN CONTINUED FRACTIONS.
- Authors
SHANG, LEI; WU, MIN
- Abstract
Let ψ : ℕ → ℝ + be a function satisfying ψ (n) → ∞ as n → ∞. Write E (ψ) : = x ∈ (0 , 1) : lim n → ∞ T n (x) ψ (n) = 1 , where T n (x) denotes the largest partial quotient among the first n terms in the continued fraction expansion of x. We prove that E (ψ) has full Hausdorff dimension for a large class of functions ψ , which strengthens the result of [L. Fang and J. Liu, On the largest partial quotients in continued fraction expansions, Fractals29 (2021) 2150099.].
- Subjects
FRACTAL dimensions; CONTINUED fractions
- Publication
Fractals, 2022, Vol 30, Issue 4, p1
- ISSN
0218-348X
- Publication type
Article
- DOI
10.1142/S0218348X22500955