## Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  238.10002
Autor:  Erdös, Paul; Ryavec, C.
Title:  A characterization of finitely monotonic additive functions. (In English)
Source:  J. Lond. Math. Soc., II. Ser. 5, 362-367 (1972).
Review:  Let f(n) be a real valued function. f(n) is additive if f(a · b) = f(a)+f(b) for (a,b) = 1. f(n) is said to be finitely monotonic if there exists an infinite sequence xk ––> oo and a positive constant \lambda so that for each k there are integers 1 \leq a1 < ... < an \leq xk, n > \lambda xk and f(a1) \leq f(a2) \leq ... \leq f(an). The authors prove: An addiitve function f(n) is finitely monotonic if and only if f(n) = c log n+g(n) where sumg(p) \ne 0 1/p < oo.
Classif.:  * 11A25 Arithmetic functions, etc.

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag