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JOURNALS // Matematicheskie Zametki // Archive

Mat. Zametki, 2018 Volume 103, Issue 5, Pages 750–764 (Mi mzm10547)

This article is cited in 1 paper

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

O. A. Petruschov

Moscow

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.

Keywords: power series, multiplicative function, Dirichlet series.

UDC: 511.35+517.537.3

Received: 07.09.2014
Revised: 06.12.2017

DOI: 10.4213/mzm10547


 English version:
Mathematical Notes, 2018, 103:5, 797–810

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© Steklov Math. Inst. of RAS, 2026