Folded continued fractions

“…Real numbers such as ξ were shown to be transcendental in [27] thanks to the so-called Mahler method (the observation that Ridout's Theorem [34] also implies that such numbers are transcendental was for instance done in [1]). Consequently, we get the transcendence of a family of continued fractions whose shape arises from paperfolding sequences; a fact mentioned in [31]. The following result has the same flavour though it is obtained in a totally different way.…”

Section: Annales De L'institut Fouriermentioning

confidence: 77%

“…As a consequence, the authors of [31] precisely described the continued fraction expansion of the real number ξ = 2 n 0 e n 2 −2 n . In particular, they proved that such an expansion is also closely related to the sequence f and called it a "folded continued fraction".…”

Section: Annales De L'institut Fouriermentioning

confidence: 99%

Continued fractions and transcendental numbers

Adamczewski¹,

Bugeaud²,

Davison³

2006

Ann. inst. Fourier

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“…The lemma may be deduced from results proved by Niederreiter in [7]; however, we give a simple proof which follows the approach taken by van der Poorten and Shallit in [10].…”

Section: Continued Fractionsmentioning

confidence: 96%

Polynomials with Odd Orthogonal Multiplicity

Lauder

1998

Finite Fields and Their Applications

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Let the orthogonal multiplicity of a monic polynomial g over a field % be the number of polynomials f over %, coprime to g and of degree less than that of g, such that all the partial quotients of the continued fraction expansion of f/g are of degree 1. Polynomials with positive orthogonal multiplicity arise in stream cipher theory, part of cryptography, as the minimal polynomials of the initial segments of sequences which have perfect linear complexity profiles. This paper focuses on polynomials which have odd orthogonal multiplicity; such polynomials are characterized and a lower bound on their orthogonal multiplicity is given. A special case of a conjecture on rational functions over the finite field of two elements with partial quotients of degree 1 or 2 in their continued fraction expansion is also proved.1998 Academic Press

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Folded continued fractions

Cited by 56 publications

References 11 publications

On a mixed Littlewood conjecture in Diophantine approximation

On a mixed Littlewood conjecture in Diophantine approximation

Continued fractions and transcendental numbers

Polynomials with Odd Orthogonal Multiplicity

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