Irrational numbers of constant type -- a new characterization.
Mukherjee, Manash, Karner, Gunther (1998)
The New York Journal of Mathematics [electronic only]
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Mukherjee, Manash, Karner, Gunther (1998)
The New York Journal of Mathematics [electronic only]
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George T. Diderrich (1979)
Aequationes mathematicae
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Barrabés, Esther, Juher, David (2005)
International Journal of Mathematics and Mathematical Sciences
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Claudio Bonanno, Stefano Isola (2009)
Colloquium Mathematicae
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This paper is devoted to a systematic study of a class of binary trees encoding the structure of rational numbers both from arithmetic and dynamical point of view. The paper is divided into three parts. The first one is mainly expository and consists in a critical review of rather standard topics such as Stern-Brocot and Farey trees and their connections with continued fraction expansion and the question mark function. In the second part we introduce two classes of (invertible and non-invertible)...
James Mc Laughlin (2008)
Acta Arithmetica
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Boris Adamczewski (2010)
Acta Arithmetica
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Ernest S. Croot III (2001)
Acta Arithmetica
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Takao Komatsu (2003)
Acta Arithmetica
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Florin P. Boca, Joseph Vandehey (2012)
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.
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.
J. Mc Laughlin, Nancy J. Wyshinski (2005)
Acta Arithmetica
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Yuanhong Chen, Yu Sun, Xiaojun Zhao (2015)
Acta Arithmetica
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Amedeo Scremin (2006)
Acta Arithmetica
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Denis, Remy Y. (1990)
International Journal of Mathematics and Mathematical Sciences
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