Distribution functions of ratio sequences, III

作者：Balaz Vladimir^*; Misik Ladislav; Strauch Oto; Toth Janos T

来源：Publicationes Mathematicae-Debrecen, 2013, 82(3-4): 511-529.

DOI：10.5486/PMD.2013.4770

• blocks sequence
• distribution function
• asymptotic density

In this paper we study the distribution functions g(x) of the sequence of blocks X-n = (x(1/)x(n), x(2)/x(n), ... , x(n)/x(n)), n = 1, 2, ... , where x(n) is an increasing sequence of positive integers. Assuming that the lower asymptotic density (sic) of x(n), is positive, we find the optimal lower and upper bounds of g(x). As an application, we also get the,optimal bounds of limit points 1/n Sigma(n)(i=1) x(1)/x(n), n = 1, 2, ...

• 出版日期2013-4
• 单位中国人民解放军信息工程大学