Transcendental p-adic continued fractions
نویسندگان
چکیده
منابع مشابه
P -adic Continued Fractions
Continued fractions in R have a single definition and algorithms for approximating them are well known. There also exists a well known result which states that √ m, m ∈ Q, always has a periodic continued fraction representation. In Qp, the field of p-adics, however, there are competing and non-equivalent definitions of continued fractions and no single algorithm exists which always produces a p...
متن کاملContinued fractions and transcendental numbers
It is widely believed that the continued fraction expansion of every irrational algebraic number α either is eventually periodic (and we know that this is the case if and only if α is a quadratic irrational), or it contains arbitrarily large partial quotients. Apparently, this question was first considered by Khintchine in [22] (see also [6,39,41] for surveys including a discussion on this subj...
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We establish new combinatorial transcendence criteria for continued fraction expansions. Let α = [0; a1, a2, . . .] be an algebraic number of degree at least three. One of our criteria implies that the sequence of partial quotients (a`)`≥1 of α is not ‘too simple’ (in a suitable sense) and cannot be generated by a finite automaton. Résumé. Nous établissons de nouveaux critères combinatoires de ...
متن کاملP-adic Continued Fractions and a P-adic Behavior of Quasi-periodic Dynamical Systems
In this paper we introduce p-adic continued fractions and its application to quasi-periodic dynamical systems. Investigating the recurrent properties of its orbits, we use the lattice theory, which has direct applications to cryptography. At last we show some numerical calculations of p-adic continued fractions and Gauss reduction algorithm by using the open source software Sage.
متن کاملTranscendental Continued Fractions over IKp(X)
The purpose behind this work is to construct from a family of algebraic formal power series of degree more than 2, a family of transcendental fractions over IKp(X).
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ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2017
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-017-1859-2