Geodesic
On the Behavior of a Power Series with Completely Multiplicative Coefficients near the Unit Circle
Matematičeskie zametki, Tome 103 (2018) no. 5, pp. 750-764

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Power series whose coefficients are values of completely multiplicative functions from a general class determined by a small number of constraints are studied. The paper contains proofs of asymptotic estimates as such a power series tends to the roots of $1$ along the radii of the unit circle, whence, in particular, it follows that these series cannot be extended beyond the unit disk.
Keywords: power series, multiplicative function, Dirichlet series. 
@article{MZM_2018_103_5_a9,
     author = {O. A. Petruschov},
     title = {On the {Behavior} of a {Power} {Series} with {Completely} {Multiplicative} {Coefficients} near the {Unit} {Circle}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {750--764},
     publisher = {mathdoc},
     volume = {103},
     number = {5},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_103_5_a9/}
}
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O. A. Petruschov. On the Behavior of a Power Series with Completely Multiplicative Coefficients near the Unit Circle. Matematičeskie zametki, Tome 103 (2018) no. 5, pp. 750-764. http://geodesic.mathdoc.fr/item/MZM_2018_103_5_a9/