Geodesic
A Remark on a Certain Class of Arithmetic Functions
Publications de l'Institut Mathématique, _N_S_46 (1989) no. 60, p. 55 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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Let $a(n)$ be an arithmetic function such that $ \sum_{n=1}^{\infty}a(n)/n^s=f(s)łog 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 zeta-like function, $h(s)$ is analytic and bounded for Re $(s)\ge 1/2+\varepsilon$. Then $ \sum_{nłe x}a(n)=xłeft[b_1/łog x+\cdots+b_m/łog^mx+O(1/łog^{m+1}x)\right] $ with arbitrary fixed $m\ge 1$, $b_1=f(1)$ and computable constants $b_2,\cdots,b_m$.
Classification : 11N64 11A25 
@article{PIM_1989_N_S_46_60_a8,
     author = {Piotr Zarzycki},
     title = {A {Remark} on a {Certain} {Class} of {Arithmetic} {Functions}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {55 },
     year = {1989},
     volume = {_N_S_46},
     number = {60},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1989_N_S_46_60_a8/}
}
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Piotr Zarzycki. A Remark on a Certain Class of Arithmetic Functions. Publications de l'Institut Mathématique, _N_S_46 (1989) no. 60, p. 55 . http://geodesic.mathdoc.fr/item/PIM_1989_N_S_46_60_a8/