Displaying similar documents to “Continued fractions and transcendental numbers”

Palindromic continued fractions

Boris Adamczewski, Yann Bugeaud (2007)

Annales de l’institut Fourier

Similarity:

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

Similarity:

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...

Symmetry and folding of continued fractions

Alfred J. Van der Poorten (2002)

Journal de théorie des nombres de Bordeaux

Similarity:

Michel Mendès France's “Folding Lemma” for continued fraction expansions provides an unusual explanation for the well known symmetry in the expansion of a quadratic irrational integer.

'The mother of all continued fractions'

Karma Dajani, Cor Kraaikamp (2000)

Colloquium Mathematicae

Similarity:

We give the relationship between regular continued fractions and Lehner fractions, using a procedure known as insertion}. Starting from the regular continued fraction expansion of any real irrational x, when the maximal number of insertions is applied one obtains the Lehner fraction of x. Insertions (and singularizations) show how these (and other) continued fraction expansions are related. We also investigate the relation between Lehner fractions and the Farey expansion (also known...