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

 

$\cos\pi\lambda$ again


Author: P. C. Fenton
Journal: Proc. Amer. Math. Soc. 131 (2003), 1875-1880
MSC (2000): Primary 30D15
Published electronically: November 6, 2002
MathSciNet review: 1955276
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Abstract: It is shown that if, for an entire function,

\begin{displaymath}\liminf_{r\to\infty} \logEM(r)/r^{\lambda} = 0 \end{displaymath}

where $0< \lambda <1$, then

\begin{displaymath}\limsup_{r\to\infty}(\log m(r)-\cos\pi\lambda\log M(r))/\log r = \infty. \end{displaymath}

In the proof, the zeros of the function are redistributed to minimize the large values of $\log m(r) -\cos\pi\lambda\log M(r)$.


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Additional Information

P. C. Fenton
Affiliation: Department of Mathematics, University of Otago, P.O. Box 56, Dunedin, New Zealand

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06750-3
PII: S 0002-9939(02)06750-3
Received by editor(s): February 7, 2002
Published electronically: November 6, 2002
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2002 American Mathematical Society