# zbMATH — the first resource for mathematics

A new proof of Erdős’s theorem on monotone multiplicative functions. (English) Zbl 0614.10001
P. Erdős proved [Ann. Math., II. Ser. 47, 1-20 (1946; Zbl 0062.079)] that if f is multiplicative and increasing then $$f(n)=n^{\alpha}$$ for some $$\alpha\geq 0$$. The author gives a short proof of this theorem.
Reviewer: D.Wolke

##### MSC:
 11A25 Arithmetic functions; related numbers; inversion formulas
##### Keywords:
completely multiplicative functions
Full Text: