Displaying similar documents to “Episturmian morphisms and a Galois theorem on continued fractions”

Leaping convergents of Hurwitz continued fractions

Takao Komatsu (2011)

Discussiones Mathematicae - General Algebra and Applications

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Let pₙ/qₙ = [a₀;a₁,...,aₙ] be the n-th convergent of the continued fraction expansion of [a₀;a₁,a₂,...]. Leaping convergents are those of every r-th convergent p r n + i / q r n + i (n = 0,1,2,...) for fixed integers r and i with r ≥ 2 and i = 0,1,...,r-1. The leaping convergents for the e-type Hurwitz continued fractions have been studied. In special, recurrence relations and explicit forms of such leaping convergents have been treated. In this paper, we consider recurrence relations and explicit forms...

Leaping convergents of Tasoev continued fractions

Takao Komatsu (2011)

Discussiones Mathematicae - General Algebra and Applications

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Denote the n-th convergent of the continued fraction by pₙ/qₙ = [a₀;a₁,...,aₙ]. We give some explicit forms of leaping convergents of Tasoev continued fractions. For instance, [0;ua,ua²,ua³,...] is one of the typical types of Tasoev continued fractions. Leaping convergents are of the form p r n + i / q r n + i (n=0,1,2,...) for fixed integers r ≥ 2 and 0 ≤ i ≤ r-1.

Substitution invariant sturmian bisequences

Bruno Parvaix (1999)

Journal de théorie des nombres de Bordeaux

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We prove that a Sturmian bisequence, with slope α and intercept ρ , is fixed by some non-trivial substitution if and only if α is a Sturm number and ρ belongs to ℚ ( α ) . We also detail a complementary system of integers connected with Beatty bisequences.

On the length of the continued fraction for values of quotients of power sums

Pietro Corvaja, Umberto Zannier (2005)

Journal de Théorie des Nombres de Bordeaux

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Generalizing a result of Pourchet, we show that, if α , β are power sums over ℚ satisfying suitable necessary assumptions, the length of the continued fraction for α ( n ) / β ( n ) tends to infinity as n → ∞ . This will be derived from a uniform Thue-type inequality for the rational approximations to the rational numbers α ( n ) / β ( n ) , n ∈ ℕ .

Palindromic continued fractions

Boris Adamczewski, Yann Bugeaud (2007)

Annales de l’institut Fourier

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In the present work, we investigate real numbers whose sequence of partial quotients enjoys some combinatorial properties involving the notion of palindrome. We provide three new transendence criteria, that apply to a broad class of continued fraction expansions, including expansions with unbounded partial quotients. Their proofs heavily depend on the Schmidt Subspace Theorem.

Continued fractions and transcendental numbers

Boris Adamczewski, Yann Bugeaud, Les Davison (2006)

Annales de l’institut Fourier

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The main purpose of this work is to present new families of transcendental continued fractions with bounded partial quotients. Our results are derived thanks to combinatorial transcendence criteria recently obtained by the first two authors in [3].