On the period of the continued fraction for values of the square root of power sums
Amedeo Scremin (2006)
Acta Arithmetica
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Amedeo Scremin (2006)
Acta Arithmetica
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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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Florin P. Boca, Joseph Vandehey (2012)
Acta Arithmetica
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James Mc Laughlin, Peter Zimmer (2007)
Acta Arithmetica
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J. Mc Laughlin, Nancy J. Wyshinski (2005)
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.
Komatsu, Takao (2006)
Mathematica Pannonica
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Denis, Remy Y. (1990)
International Journal of Mathematics and Mathematical Sciences
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Jacobson, Michael J.jun., Williams, Hugh C. (2000)
Experimental Mathematics
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S. G. Dani (2015)
Acta Arithmetica
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We introduce a general framework for studying continued fraction expansions for complex numbers, and establish some results on the convergence of the corresponding sequence of convergents. For continued fraction expansions with partial quotients in a discrete subring of ℂ an analogue of the classical Lagrange theorem, characterising quadratic surds as numbers with eventually periodic continued fraction expansions, is proved. Monotonicity and exponential growth are established for the...
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.
Ustinov, A.V. (2005)
Journal of Mathematical Sciences (New York)
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Yuanhong Chen, Yu Sun, Xiaojun Zhao (2015)
Acta Arithmetica
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