A note on Farey fractions with denominators in arithmetic progressions
Dmitry A. Badziahin, Alan K. Haynes (2011)
Acta Arithmetica
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Dmitry A. Badziahin, Alan K. Haynes (2011)
Acta Arithmetica
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K. Dajani, C. Kraaikamp, V. Masarotto (2012)
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Xue Hai Hu, Jun Wu (2009)
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Lisa Lorentzen (1992)
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Florin P. Boca, Joseph Vandehey (2012)
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Takao Komatsu (2003)
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Yuanhong Chen, Yu Sun, Xiaojun Zhao (2015)
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James Mc Laughlin (2008)
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Javier Docampo Rey (2009)
Revue d'histoire des mathématiques
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This paper contains a critical edition of a short commercial arithmetic written in Castilian (ca. 1400). The manuscript has certain characteristic features, like the presence of composite fractions, that distinguishes it from other known treatises of the Iberian peninsula. The document appears to improve considerably our knowledge of the origins and the transmission of vernacular commercial arithmetic in Europe.
Boris Adamczewski (2010)
Acta Arithmetica
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J. Mc Laughlin, Nancy J. Wyshinski (2005)
Acta Arithmetica
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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...
Denis, Remy Y. (1990)
International Journal of Mathematics and Mathematical Sciences
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Boonrod Yuttanan (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.
Zongduo Dai, Ping Wang, Kunpeng Wang, Xiutao Feng (2007)
Acta Arithmetica
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