Displaying similar documents to “Construction of families of long continued fractions.”

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].

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.

Rosen fractions and Veech groups, an overly brief introduction

Thomas A. Schmidt (2009)

Actes des rencontres du CIRM

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We give a very brief, but gentle, sketch of an introduction both to the Rosen continued fractions and to a geometric setting to which they are related, given in terms of Veech groups. We have kept the informal approach of the talk at the Numerations conference, aimed at an audience assumed to have heard of neither of the topics of the title. The Rosen continued fractions are a family of continued fraction algorithms, each gives expansions of real numbers in terms of elements...