A new class of continued fraction expansions
Cor Kraaikamp (1991)
Acta Arithmetica
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Cor Kraaikamp (1991)
Acta Arithmetica
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Karma Dajani, Cor Kraaikamp (2000)
Colloquium Mathematicae
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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...
J. Allouche, M. Mendès France, A. van der Poorten (1991)
Acta Arithmetica
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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].
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.
Hitoshi Nakada (1990)
Acta Arithmetica
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Mollin, R.A. (2003)
Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]
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Dominique Barbolosi, Hendrik Jager (1994)
Journal de théorie des nombres de Bordeaux
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