关于Hausdorff维数小值的bourgin - kontorovich定理的强化

IF 0.6 4区数学 Q3 MATHEMATICS

Functional Analysis and Its Applications Pub Date : 2022-07-29 DOI:10.1134/S0016266322010051

I. D. Kan

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引用次数: 3

摘要

设\(\mathfrak{D}_\mathbf{A}(N)\)为不超过\(N\)的所有整数的集合，并且等于具有有限连分数展开式的正有理数的不可约分母，其中所有部分商都属于有限数字字母\(\mathbf{A}\)。获得了基数\(|\mathfrak{D}_\mathbf{A}(N)|\)的新下界，其非平凡部分比先前已知的下界提高了28%.

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Strengthening of the Bourgain–Kontorovich Theorem on Small Values of Hausdorff Dimension

Let \(\mathfrak{D}_\mathbf{A}(N)\) be the set of all integers not exceeding \(N\) and equal to irreducible denominators of positive rational numbers with finite continued fraction expansions in which all partial quotients belong to a finite number alphabet \(\mathbf{A}\). A new lower bound for the cardinality \(|\mathfrak{D}_\mathbf{A}(N)|\) is obtained, whose nontrivial part improves that known previously by up to 28%.

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来源期刊

Functional Analysis and Its Applications 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Functional Analysis and Its Applications publishes current problems of functional analysis, including representation theory, theory of abstract and functional spaces, theory of operators, spectral theory, theory of operator equations, and the theory of normed rings. The journal also covers the most important applications of functional analysis in mathematics, mechanics, and theoretical physics.