Displaying similar documents to “A new class of continued fraction expansions”

'The mother of all continued fractions'

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...

Symmetry and folding of continued fractions

Alfred J. Van der Poorten (2002)

Journal de théorie des nombres de Bordeaux

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Michel Mendès France's “Folding Lemma” for continued fraction expansions provides an unusual explanation for the well known symmetry in the expansion of a quadratic irrational integer.

Continued fractions on the Heisenberg group

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.

Continued fraction expansions for complex numbers-a general approach

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...