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Abstract. Let $f$ and $g$ be completely additive functions, $\delta(n)=g([\sqrt{2}n])-f(n)-C, C\in\rr $. If $\lim_{x\to\infty }{1\over x}\sharp\{n\le x | \| \delta(n)\| > \epsilon\}=0$ for every $\epsilon >0$, then $f(n)=g(n)=A\log n$, where $A={2C/{\log2}}$.
DOI: 10.14232/actasm-014-327-y
AMS Subject Classification
(1991): 11K65, 11N37, 11N64
Keyword(s):
completely additive functions,
multiplicative group
Received November 24, 2014, and in revised form March 29, 2015. (Registered under 77/2014.)
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