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p-adische Kettenbrüche und Irrationalität p-adischer Zahlen.

P. Bundschuh (1977)

Elemente der Mathematik

Palindromic continued fractions

Boris Adamczewski, Yann Bugeaud (2007)

Annales de l’institut Fourier

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.

Periodic Jacobi-Perron expansions associated with a unit

Brigitte Adam, Georges Rhin (2011)

Journal de Théorie des Nombres de Bordeaux

We prove that, for any unit $ϵ$ in a real number field $K$ of degree $n + 1$ , there exits only a finite number of n-tuples in $K^{n}$ which have a purely periodic expansion by the Jacobi-Perron algorithm. This generalizes the case of continued fractions for $n = 1$ . For $n = 2$ we give an explicit algorithm to compute all these pairs.

Periodic multiplicative algorithms of Selmer type.

Schweiger, Fritz (2005)

Integers

Periodicity of p-adic continued fractions.

B.M.M. de Weger (1988)

Elemente der Mathematik

Polynomial continued fractions

D. Bowman, J. Mc Laughlin (2002)

Acta Arithmetica

Products and quotients of numbers with small partial quotients

Stephen Astels (2002)

Journal de théorie des nombres de Bordeaux

For any positive integer $m$ let $F (m)$ denote the set of numbers with all partial quotients (except possibly the first) not exceeding $m$ . In this paper we characterize most products and quotients of sets of the form $F (m)$ .