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Matematicheskie Zametki, 2016, Volume 100, Issue 6, Pages 887–899
DOI: https://doi.org/10.4213/mzm10682 (Mi mzm10682) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Asymptotic Expansion of Certain Power Series with Multiplicative Coefficients near the Unit Circle

O. A. Petruschov
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DOI: https://doi.org/10.4213/mzm10682
Abstract: An asymptotic theorem important for the study of many power series with multiplicative coefficients is proved. Examples of concrete series to which the theorem can be applied are given. It is shown that power series of many classical arithmetic sequences can be expanded in asymptotic series as the variable tends to the roots of unity along the radii of the unit circle.
Keywords: power series, multiplicative function, classical arithmetic function, asymptotics, sum of divisors.
Received: 15.01.2015
Revised: 09.03.2016
English version:
Mathematical Notes, 2017, Volume 101, Issue 2, Pages 297–309
DOI: https://doi.org/10.1134/S0001434617010345
Bibliographic databases:
Document Type: Article
UDC: 511.35+517.537.3
Language: Russian
Citation: O. A. Petruschov, “Asymptotic Expansion of Certain Power Series with Multiplicative Coefficients near the Unit Circle”, Mat. Zametki, 100:6 (2016), 887–899; Math. Notes, 101:2 (2017), 297–309
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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