p-adische Kettenbrüche und Irrationalität p-adischer Zahlen.
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P. Bundschuh (1977)
Elemente der Mathematik
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.
Brigitte Adam, Georges Rhin (2011)
Journal de Théorie des Nombres de Bordeaux
We prove that, for any unit in a real number field of degree , there exits only a finite number of n-tuples in which have a purely periodic expansion by the Jacobi-Perron algorithm. This generalizes the case of continued fractions for . For we give an explicit algorithm to compute all these pairs.
Schweiger, Fritz (2005)
Integers
B.M.M. de Weger (1988)
Elemente der Mathematik
D. Bowman, J. Mc Laughlin (2002)
Acta Arithmetica
Stephen Astels (2002)
Journal de théorie des nombres de Bordeaux
For any positive integer let denote the set of numbers with all partial quotients (except possibly the first) not exceeding . In this paper we characterize most products and quotients of sets of the form .
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