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Distribution functions of ratio sequences. An expository paper

   | 19 feb 2016
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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.

eISSN:
1210-3195
Lingua:
Inglese
Frequenza di pubblicazione:
3 volte all'anno
Argomenti della rivista:
Mathematics, General Mathematics