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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
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
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
Linking options:
https://www.mathnet.ru/eng/mzm10682https://doi.org/10.4213/mzm10682 https://www.mathnet.ru/eng/mzm/v100/i6/p887
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Abstract page: | 224 | Full-text PDF : | 41 | References: | 47 | First page: | 17 |
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