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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A version of Fabry's theorem for power series with regularly varying coefficients


Author: Alexandre Eremenko
Journal: Proc. Amer. Math. Soc. 136 (2008), 4389-4394
MSC (2000): Primary 30B10, 30B40
Published electronically: July 24, 2008
MathSciNet review: 2431054
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Abstract: For real power series whose non-zero coefficients satisfy $ \vert a_m\vert^{1/m} \to~1$, we prove a stronger version of Fabry's theorem relating the frequency of sign changes in the coefficients and analytic continuation of the sum of the power series.


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Additional Information

Alexandre Eremenko
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email: eremenko@math.purdue.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09652-4
PII: S 0002-9939(08)09652-4
Received by editor(s): November 19, 2007
Published electronically: July 24, 2008
Additional Notes: The author was supported by NSF grant DMS-0555279.
Communicated by: Mario Bonk
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.