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.
Citation:
O. A. Petruschov, “On the Behavior of a Power Series with Completely Multiplicative Coefficients near the Unit Circle”, Mat. Zametki, 103:5 (2018), 750–764; Math. Notes, 103:5 (2018), 797–810
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\by O.~A.~Petruschov
\paper On the Behavior of a Power Series with Completely Multiplicative Coefficients near the Unit Circle
\jour Mat. Zametki
\yr 2018
\vol 103
\issue 5
\pages 750--764
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\jour Math. Notes
\yr 2018
\vol 103
\issue 5
\pages 797--810
\crossref{https://doi.org/10.1134/S0001434618050127}
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Linking options:
https://www.mathnet.ru/eng/mzm10547
https://doi.org/10.4213/mzm10547
https://www.mathnet.ru/eng/mzm/v103/i5/p750
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