On the average length of finite continued fractions
نویسندگان
چکیده
منابع مشابه
The Euclidean algorithm and finite continued fractions
Fowler [22] Measure theory of continued fractions: Einsiedler and Ward [19, Chapter 3] and Iosifescu and Kraaikamp [35, Chapter 1]. In harmonic analysis and dynamical systems, we usually care about infinite continued fractions because we usually care about the Lebesgue measure of a set defined by some conditions on the convergents or partial quotients of a continued fraction. For some questions...
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Letting x = [a1(x), a2(x), . . .] denote the continued fraction expansion of an irrational number x ∈ (0, 1), Khinchin proved that Sn(x) = ∑n k=1 ak(x) ∼ 1 log 2 n logn in measure, but not for almost every x. Diamond and Vaaler showed that removing the largest term from Sn(x), the previous asymptotics will hold almost everywhere, showing the crucial influence of the extreme terms of Sn(x) on th...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1974
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-26-1-47-57