Geodesic
Asymptotic Expansion of Certain Power Series with Multiplicative Coefficients near the Unit Circle
Matematičeskie zametki, Tome 100 (2016) no. 6, pp. 887-899

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An asymptotic theorem important for the study of many power series with multiplicative coefficients is proved. Examples of concrete series to which the theorem can be applied are given. It is shown that power series of many classical arithmetic sequences can be expanded in asymptotic series as the variable tends to the roots of unity along the radii of the unit circle.
Keywords: power series, multiplicative function, classical arithmetic function, asymptotics, sum of divisors. 
@article{MZM_2016_100_6_a10,
     author = {O. A. Petruschov},
     title = {Asymptotic {Expansion} of {Certain} {Power} {Series} with {Multiplicative} {Coefficients} near the {Unit} {Circle}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {887--899},
     publisher = {mathdoc},
     volume = {100},
     number = {6},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_100_6_a10/}
}
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O. A. Petruschov. Asymptotic Expansion of Certain Power Series with Multiplicative Coefficients near the Unit Circle. Matematičeskie zametki, Tome 100 (2016) no. 6, pp. 887-899. http://geodesic.mathdoc.fr/item/MZM_2016_100_6_a10/