and let

One notes that \theta(k,\epsilon) \leq \rho(k,\epsilon) and \sup_{k \geq k0}\rho(k,\epsilon) \leq \delta(k₀,\epsilon). It is shown that if \rho(k,\epsilon) ––> 0 (k ––> oo) for all \epsilon > 0, then sum_p\frac{g(p)^r}{p} < oo for every r \geq 1, thus considerably stregthening a result previously obtained by the authors [Acta Math. Acad. Sci. Hung. 33, 345-359 (1979; Zbl 417.10039)]. Among other results obtained (space limitations unfortunately preclude giving the complete list), we find the following: If g(p) = 1/p for promes p then

where \lambda_k = 3/ log log k, while if g(p) = 1(p^\delta, 0 < \delta < 1, and \rho > 0 is an arbitrary constant, then

In the paper reviewed above the authors stated erroneously that Theorem 1 is a consequence of Theorem 1'. In fact, the converse implication is true: Theorem 1 implies Theorem 1'. A proof of Theorem 1 is given.
Reviewer:  B.Garrison
Classif.:  * 11N37 Asymptotic results on arithmetic functions
                   11K65 Arithmetic functions (probabilistic number theory)
Keywords:  distribution of maximal value; strongly additive function

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