ACTA issues

On the multiplicative group generated by $\big\{{[\sqrt{2}n]\over n} \big | n\in{\msbm N}\big\}$. II

I. Kátai, B. M. Phong

Acta Sci. Math. (Szeged) 81:3-4(2015), 431-436

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.)