PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 46(60), pp. 5558 (1989) 

A remark on a certain class of arithmetic functionsPiotr ZarzyckiDepartment of Mathematics, University of Gda\'nsk, 80952 Gda\'nsk, PolandAbstract: Let $a(n)$ be an arithmetic function such that $$ \sum_{n=1}^{\infty}a(n)/n^s=f(s)\log g(s)+h(s), $$ where $f(s)$ is analytic for Re\,$(s)>1/2$ and bounded for Re\,$(s)\ge 1/2+\varepsilon$, $g(s)$ is a zetalike function, $h(s)$ is analytic and bounded for Re\,$(s)\ge 1/2+\varepsilon$. Then $$ \sum_{n\le x}a(n)=x\left[b_1/\log x+\cdots+b_m/\log^mx+O(1/\log^{m+1}x)\right] $$ with arbitrary fixed $m\ge 1$, $b_1=f(1)$ and computable constants $b_2,\cdots,b_m$. Classification (MSC2000): 11N64; 11A25 Full text of the article:
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