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2020 On the behavior of power series with positive completely multiplicative coefficients
Oleg A. Petrushov
Mosc. J. Comb. Number Theory 9(2): 147-162 (2020). DOI: 10.2140/moscow.2020.9.147

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 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.

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Oleg A. Petrushov. "On the behavior of power series with positive completely multiplicative coefficients." Mosc. J. Comb. Number Theory 9 (2) 147 - 162, 2020. https://doi.org/10.2140/moscow.2020.9.147

Information

Received: 12 September 2018; Revised: 21 March 2020; Accepted: 5 April 2020; Published: 2020
First available in Project Euclid: 17 September 2020

zbMATH: 07211444
MathSciNet: MR4096118
Digital Object Identifier: 10.2140/moscow.2020.9.147

Subjects:
Primary: 11N37
Secondary: 30B30

Rights: Copyright © 2020 Mathematical Sciences Publishers

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