共查询到20条相似文献,搜索用时 15 毫秒
1.
Tanguy Rivoal 《Monatshefte für Mathematik》2011,164(3):325-360
We introduce new series (of the variable ??) that enable to measure the irregularity of distribution of the sequence of fractional parts {n??}. A detailed analysis of the convergence and divergence of these series is done, depending mainly on the convergents of ??. As a by product, we obtain new Fourier series of square integrable functions that converge almost everywhere but at no rational number. 相似文献
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Guoyou Qian 《Comptes Rendus Mathematique》2017,355(11):1127-1132
Let be a strictly increasing sequence of positive integers ( if ). In 1978, Borwein showed that for any positive integer n, we have , with equality occurring if and only if for . Let be an integer. In this paper, we investigate the sum and show that for any positive integer n, where is a constant depending on r and n. Further, for any integer , we also give a characterization of the sequence such that the equality holds. 相似文献
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Let g>1 be an integer and sg(m) be the sum of digits in base g of the positive integer m. In this paper, we study the positive integers n such that sg(n) and sg(kn) satisfy certain relations for a fixed, or arbitrary positive integer k. In the first part of the paper, we prove that if n is not a power of g, then there exists a nontrivial multiple of n say kn such that sg(n)=sg(kn). In the second part of the paper, we show that for any K>0 the set of the integers n satisfying sg(n)?Ksg(kn) for all k∈N is of asymptotic density 0. This gives an affirmative answer to a question of W.M. Schmidt. 相似文献
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Rita Giuliano-Antonini Georges Grekos Ladislav Mišík 《Czechoslovak Mathematical Journal》2007,57(3):947-962
The continuity of densities given by the weight functions n
α
, α ∈ [−1, ∞[, with respect to the parameter α is investigated.
This work is supported by MIUR Italy, Program Barrande n. 2003-009-2, MSM6198898701 and GA ČR no. 201/04/0381. 相似文献
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Helmut Werner 《Mathematische Zeitschrift》1964,86(4):317-326
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Leiba Rodman 《Integral Equations and Operator Theory》1978,1(3):400-414
A sufficient condition (in terms of spectral behaviour) for existence of common multiples of monic operator polynomials is given. 相似文献
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The object of this paper is to extend some results concerning the univalence, starlikeness, and convexity of rational functions recently obtained by Reade, Silverman, and Todorov. The domain of variability of log{f(z)/z} for a fixedz and for such functionsf ranging over the class of λ-spirallike functions of order α are also determined. 相似文献
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Joseph Zaks 《Aequationes Mathematicae》1989,37(2-3):259-266
Summary LetQ
4 denote the graph, obtained from the rational points of the 4-space, by connecting two points iff their Euclidean distance is one. It has been known that its chromatic number is 4. We settle a problem of P. Johnson, showing that in every four-colouring of this graph, every colour class is every-where dense. 相似文献
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Václav Kijonka 《Mathematica Slovaca》2008,58(2):155-164
In the paper continuous variants of densities of sets of positive integers are introduced, some of their properties are studied
and formula for their calculation is proved.
Supported by the grant GA CR no. 201/04/0381. 相似文献
19.
Jun Wang 《Journal of Mathematical Analysis and Applications》2011,379(2):637-812
Let K(a) be the symmetrical Cantor set generated by ?0(x)=ax and ?1(x)=ax+(1−a), where 0<a<1/2. Let s be the Hausdorff dimension of K(a) and μ the Cantor measure. In this paper, under the hypothesis that a is slightly greater than 1/3, we obtain the explicit formulas of the upper and lower s-densities Θ?s(μ,x), for every point x∈K(a). Moreover, we describe the range of a key quantity τ(x) in these formulas. 相似文献
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A. Bahri M. Bendersky F. R. Cohen S. Gitler 《Proceedings of the Steklov Institute of Mathematics》2014,286(1):219-223
In this note, it is shown that the only moment-angle complexes which are rationally elliptic are those which are products of odd spheres and a disk. 相似文献