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This article is cited in 1 scientific paper (total in 1 paper)
Certain classes of power series that cannot be analytically continued across their circle of convergence
A. I. Pavlov Steklov Mathematical Institute, Russian Academy of Sciences
Abstract:
We define, in number-theoretical terms, the class $\{M\}$ of sets of natural numbers having the properties:
1) the asymptotic density $\gamma$ of a set $M$ satisfies the inequality $0<\gamma<1$;
2) if $G(z)$ is an entire function with non-negative Taylor coefficients and not growing too fast at infinity, then the power series $\sum_{m\in M}G(m)z^m$, having radius of convergence 1, cannot be analytically continued into the domain $|z|>1$ across any arc on the circle $|z|=1$.
Received: 02.12.1995
Citation:
A. I. Pavlov, “Certain classes of power series that cannot be analytically continued across their circle of convergence”, Izv. Math., 61:4 (1997), 795–812
Linking options:
https://www.mathnet.ru/eng/im138https://doi.org/10.1070/im1997v061n04ABEH000138 https://www.mathnet.ru/eng/im/v61/i4/p119
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