Rosen fractions and Veech groups, an overly brief introduction

Thomas A. Schmidt

Displaying similar documents to “Rosen fractions and Veech groups, an overly brief introduction”

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].

Construction of families of long continued fractions.

Mollin, R.A. (2003)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

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Generalized continued fractions and orbits under the action of Hecke triangle groups

Elise Hanson, Adam Merberg, Christopher Towse, Elena Yudovina (2008)

Acta Arithmetica

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Transcendence with Rosen continued fractions

Yann Bugeaud, Pascal Hubert, Thomas A. Schmidt (2013)

Journal of the European Mathematical Society

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We give the first transcendence results for the Rosen continued fractions. Introduced over half a century ago, these fractions expand real numbers in terms of certain algebraic numbers.