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- W2013097629 abstract "Let I denote the set of all irrational numbers, θ ∈ I, and simple continued fraction expansion of θ be [a 0 , a 1 , …, a n , …]. Then a 0 is an integer and {a n } n≥1 is an infinite sequence of positive integers. Let M n (θ) = [0, a n , a n-1 , …, a 1 ] + [a n+1 , a n+2 , …]. Then the set of numbers { lim sup M n (θ) ∣ θ ∈ I} is called the Lagrange Spectrum 𝔏. Notably 3 is the first cluster point of 𝔏. Essentially lim inf 𝔏 or [Formula: see text]. Perron [Über die approximation irrationaler Zahlen durch rationale, I, S.-B. Heidelberg Akad. Wiss., Abh. 4 (1921) 17 pp; Über die approximation irrationaler Zahlen durch rationale, II, S.-B. Heidelberg Akad. Wiss., Abh.8 (1921) 12 pp.] has found that lim inf { lim sup M n (θ) ∣ θ = [a 0 , a 1 , a 2 , …, a n , …] and [Formula: see text]. This article forwards the value of lim inf{lim sup M n (θ) ∣ θ = [a 0 , a 1 , …, a n , …] and a n ≥ 4 frequently}, a long awaited cluster point of Lagrange Spectrum." @default.
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- W2013097629 date "2012-12-05" @default.
- W2013097629 modified "2023-09-25" @default.
- W2013097629 title "A NEW POINT IN LAGRANGE SPECTRUM" @default.
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- W2013097629 doi "https://doi.org/10.1142/s1793042112501382" @default.
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