منابع مشابه
Some More Long Continued Fractions, I
In this paper we show how to construct several infinite families of polynomials D(x̄, k), such that p D(x̄, k) has a regular continued fraction expansion with arbitrarily long period, the length of this period being controlled by the positive integer parameter k. We also describe how to quickly compute the fundamental units in the corresponding real quadratic fields.
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Recently, Bergman [2] provided an explicit, nonrecursive description of the partial quotients in (1), and by implication, in (2). (This description is our Theorem 3.) The purpose of this paper is to prove Bergman's result, and to provide similar results for the continued fractions given in [3] and [4]. We start off with some terminology about "strings." By a string9 we mean a (finite or infinit...
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We prove: if d/m < 2280/721, there is no curve of degree d passing through n = 10 general points with multiplicity m in P. Similar results are given for other special values of n. Our bounds can be naturally written as certain palindromic continued fractions.
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We prove singularity of some distributions of random continued fractions that correspond to iterated function systems with overlap and a parabolic point. These arose while studying the conductance of GaltonWatson trees. §
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This paper describes a method of constructing an unlimited number of infinite families of continued fraction expansions of the square root of D, an integer. The periods of these continued fractions all have identifiable sub patterns repeated a number of times according to certain parameters. For example, it is possible to construct an explicit family for the square root of D(k, l) where the per...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2007
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa127-4-4