On a theorem of Legendre in the theory of continued fractions
Dominique Barbolosi, Hendrik Jager (1994)
Journal de théorie des nombres de Bordeaux
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Dominique Barbolosi, Hendrik Jager (1994)
Journal de théorie des nombres de Bordeaux
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Andrzej Schinzel (1986)
Acta Arithmetica
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Cor Kraaikamp (1991)
Acta Arithmetica
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Florin P. Boca, Joseph Vandehey (2012)
Acta Arithmetica
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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.
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...
Takao Komatsu (2003)
Acta Arithmetica
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Boris Adamczewski (2010)
Acta Arithmetica
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James Mc Laughlin (2008)
Acta Arithmetica
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