منابع مشابه
Subexponentially increasing sums of partial quotients in continued fraction expansions
We investigate from a multifractal analysis point of view the increasing rate of the sums of partial quotients Sn(x) = ∑n j=1 aj(x), where x = [a1(x), a2(x), · · · ] is the continued fraction expansion of an irrational x ∈ (0, 1). Precisely, for an increasing function φ : N → N, one is interested in the Hausdorff dimension of the sets Eφ = { x ∈ (0, 1) : lim n→∞ Sn(x) φ(n) = 1 } . Several cases...
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Conjecturally, the only real algebraic numbers with bounded partial quotients in their regular continued fraction expansion are rationals and quadratic irrationals. We show that the corresponding statement is not true for complex algebraic numbers in a very strong sense, by constructing for every even degree d algebraic numbers of degree d that have bounded complex partial quotients in their Hu...
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Expansions that furnish increasingly good approximations to real numbers are usually related to dynamical systems. Although comparing dynamical systems seems difficult in general, Lochs was able in 1964 to relate the relative speed of approximation of decimal and regular continued fraction expansions (almost everywhere) to the quotient of the entropies of their dynamical systems. He used detail...
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There is a theory of continued fractions for Laurent series in x with coefficients in a field F . This theory bears a close analogy with classical continued fractions for real numbers with Laurent series playing the role of real numbers and the sum of the terms of non-negative degree in x playing the role of the integral part. In this paper we survey the Laurent series u, with coefficients in a...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2019
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2018.11.015