Distribution functions of ratio sequences. An expository paper

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Abstract

This expository paper presents known results on distribution functions g(x) of the sequence of blocks where xn is an increasing sequence of positive integers. Also presents results of the set G(Xn) of all distribution functions g(x). Specially:

- continuity of g(x);

- connectivity of G(Xn);

- singleton of G(Xn);

- one-step g(x);

- uniform distribution of Xn, n = 1, 2, . . . ;

- lower and upper bounds of g(x);

- applications to bounds of ;

- many examples, e.g., , where pn is the nth prime, is uniformly distributed.

The present results have been published by 25 papers of several authors between 2001-2013.

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[23] STRAUCH, O.-TÓTH, J. T.: Corrigendum to Theorem 5 of the paper “Asymptotic density of A ⊂ N and density of ratio set R(A)” (Acta Arith. 87 (1998), 67-78), Acta Arith. 103.2 (2002), 191-200.

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Tatra Mountains Mathematical Publications

The Journal of Slovak Academy of Sciences

Journal Information


CiteScore 2017: 0.37

SCImago Journal Rank (SJR) 2017: 0.363
Source Normalized Impact per Paper (SNIP) 2017: 0.482

Mathematical Citation Quotient (MCQ) 2017: 0.14

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