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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Hadamard convexity and multiplicity and location of zeros


Author: Faruk F. Abi-Khuzam
Journal: Trans. Amer. Math. Soc. 347 (1995), 3043-3051
MSC: Primary 30D20; Secondary 30D15, 30D35
MathSciNet review: 1285968
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Abstract: We consider certain questions arising from a paper of Hayman concerning quantitative versions of the Hadamard three-circle theorem for entire functions. If $ b(r)$ denotes the second derivative of $ \log M(r)$ with respect to $ \log r$, the principal contributions of this work are (i) a characterization of those entire $ f$ with nonnegative Maclaurin coefficients for which $ \lim \sup b(r) = \frac{1} {4}$ and (ii) some exploration of the relationship between multiple zeros of $ f$ and the growth of $ b(r)$.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1995-1285968-9
PII: S 0002-9947(1995)1285968-9
Article copyright: © Copyright 1995 American Mathematical Society