#### Vol. 9, No. 2, 2020

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On the behavior of power series with positive completely multiplicative coefficients

### Oleg A. Petrushov

Vol. 9 (2020), No. 2, 147–162
##### Abstract

We consider power series with positive completely multiplicative coefficients. We obtain a large family of power series that have the unit circle as natural boundary, as well as new $\Omega$-theorems for power series with positive completely multiplicative coefficients when the argument tends to roots of unity. Also $\Omega$-estimates for some partial sums of completely multiplicative functions are given.

##### Keywords
power series, positive completely multiplicative coefficients, completely multiplicative functions, Omega estimates
Primary: 11N37
Secondary: 30B30
##### Milestones
Received: 12 September 2018
Revised: 21 March 2020
Accepted: 5 April 2020
Published: 11 May 2020
##### Authors
 Oleg A. Petrushov APS RADIS Moscow Russia