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