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Abstract
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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
-theorems for power
series with positive completely multiplicative coefficients when the argument tends to roots of unity.
Also
-estimates
for some partial sums of completely multiplicative functions are given.
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Keywords
power series, positive completely multiplicative
coefficients, completely multiplicative functions, Omega
estimates
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Mathematical Subject Classification 2010
Primary: 11N37
Secondary: 30B30
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Milestones
Received: 12 September 2018
Revised: 21 March 2020
Accepted: 5 April 2020
Published: 11 May 2020
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