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On the Behavior of a Power Series with Completely Multiplicative Coefficients near the Unit Circle

Authors
  • Petrushov, O. A.1
  • 1 “Mathematical Notes,” Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia , Moscow (Russia)
Type
Published Article
Journal
Mathematical Notes
Publisher
Pleiades Publishing
Publication Date
May 01, 2018
Volume
103
Issue
5-6
Pages
797–810
Identifiers
DOI: 10.1134/S0001434618050127
Source
Springer Nature
Keywords
License
Yellow

Abstract

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.

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