Continued fractions and Parametric geometry of numbers
نویسندگان
چکیده
منابع مشابه
Continued 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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In this paper we define an equivalence relation on the set of positive irrational numbers less than 1. The relation is defined by means of continued fractions. Equivalence classes under this relation are determined by the places of some elements equal to 1 (called essential 1’s) in the continued fraction expansion of numbers. Analysis of suprema of all equivalence classes leads to a solution wh...
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We classify polycyclic dimension groups, i.e. dimension groups with the underlying group Z and n ≥ 4. Our method is based on geometry of simple geodesic lines on the Riemann surface of genus g ≥ 2. The main theorem says that every polycyclic dimension group can be indexed by single real parameter α, where α is a positive irrational modulo the action of GL(2,Z). This result is an extension of th...
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We consider a family of integer sequences generated by nonlinear recurrences of the second order, which have the curious property that the terms of the sequence, and integer multiples of the ratios of successive terms (which are also integers), appear interlaced in the continued fraction expansion of the sum of the reciprocals of the terms. Using the rapid (double exponential) growth of the ter...
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ژورنال
عنوان ژورنال: Journal de Théorie des Nombres de Bordeaux
سال: 2017
ISSN: 1246-7405,2118-8572
DOI: 10.5802/jtnb.971