Displaying similar documents to “On the Khintchine constant for centred continued fraction expansions.”

'The mother of all continued fractions'

Karma Dajani, Cor Kraaikamp (2000)

Colloquium Mathematicae

Similarity:

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...

Continued fraction expansions for complex numbers-a general approach

S. G. Dani (2015)

Acta Arithmetica

Similarity:

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...