Some new families of Tasoevian and Hurwitzian continued fractions
James Mc Laughlin (2008)
Acta Arithmetica
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James Mc Laughlin (2008)
Acta Arithmetica
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Boris Adamczewski (2010)
Acta Arithmetica
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Takao Komatsu (2003)
Acta Arithmetica
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Anton Lukyanenko, Joseph Vandehey (2015)
Acta Arithmetica
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We provide a generalization of continued fractions to the Heisenberg group. We prove an explicit estimate on the rate of convergence of the infinite continued fraction and several surprising analogs of classical formulas about continued fractions.
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.
Haas, Andrew (2005)
The New York Journal of Mathematics [electronic only]
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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].
J. Mc Laughlin, Nancy J. Wyshinski (2005)
Acta Arithmetica
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Denis, Remy Y. (1990)
International Journal of Mathematics and Mathematical Sciences
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