Displaying similar documents to “Fraction Space Revisited Нов поглед върху пространството на дробите”

Continued fractions on the Heisenberg group

Anton Lukyanenko, Joseph Vandehey (2015)

Acta Arithmetica

Similarity:

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.

Palindromic continued fractions

Boris Adamczewski, Yann Bugeaud (2007)

Annales de l’institut Fourier

Similarity:

In the present work, we investigate real numbers whose sequence of partial quotients enjoys some combinatorial properties involving the notion of palindrome. We provide three new transendence criteria, that apply to a broad class of continued fraction expansions, including expansions with unbounded partial quotients. Their proofs heavily depend on the Schmidt Subspace Theorem.

Continued fractions and transcendental numbers

Boris Adamczewski, Yann Bugeaud, Les Davison (2006)

Annales de l’institut Fourier

Similarity:

The main purpose of this work is to present new families of transcendental continued fractions with bounded partial quotients. Our results are derived thanks to combinatorial transcendence criteria recently obtained by the first two authors in [3].