Vol. 9, No. 2, 2020

Download this article
Download this article For screen
For printing
Recent Issues
Volume 10, Issue 1
Volume 9, Issue 4
Volume 9, Issue 3
Volume 9, Issue 2
Volume 9, Issue 1
Volume 8, Issue 4
Volume 8, Issue 3
Volume 8, Issue 2
Volume 8, Issue 1
The Journal
About the Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
founded and published with the
scientific support and advice of the
Moscow Institute of
Physics and Technology
ISSN (electronic): 2640-7361
ISSN (print): 2220-5438
Previously Published
Author Index
To Appear
Other MSP Journals
On the behavior of power series with positive completely multiplicative coefficients

Oleg A. Petrushov

Vol. 9 (2020), No. 2, 147–162

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 Ω-theorems for power series with positive completely multiplicative coefficients when the argument tends to roots of unity. Also Ω-estimates for some partial sums of completely multiplicative functions are given.

power series, positive completely multiplicative coefficients, completely multiplicative functions, Omega estimates
Mathematical Subject Classification 2010
Primary: 11N37
Secondary: 30B30
Received: 12 September 2018
Revised: 21 March 2020
Accepted: 5 April 2020
Published: 11 May 2020
Oleg A. Petrushov