Zentralblatt MATH

Publications of (and about) Paul Erdös
Zbl.No:  638.10049
Autor:  Babu, Gutti Jogesh; Erdös, Paul
Title:  A note on the distribution function of additive arithmetical functions in short intervals. (In English)
Source:  Can. Math. Bull. 32, No.4, 441-445 (1989).
Review:  Let f be an additive arithmetic function having a distribution F. For any sequence 1 \leq b(n) \leq n, b(n) ––> oo, let

Qn(b,f)(x) = card{n \leq m \leq n+b(n): f(m) \leq x}/b(n).

In this note, we determine the slowest growing function b so that Qn(b,f) tends weakly to F, for various f.
Reviewer:  G.J.Babu
Classif.:  * 11K65 Arithmetic functions (probabilistic number theory)
                   60F05 Weak limit theorems
Keywords:  short intervals; Erdös-Winter theorem; Erdös-Kac theorem; additive arithmetic function; distribution

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