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

 

Characteristic, maximum modulus and value distribution


Authors: W. K. Hayman and J. F. Rossi
Journal: Trans. Amer. Math. Soc. 284 (1984), 651-664
MSC: Primary 30D35; Secondary 30D20
MathSciNet review: 743737
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Abstract: Let $ f$ be an entire function such that $ \log M(r,f)\sim T(r,f)$ on a set $ E$ of positive upper density. Then $ f$ has no finite deficient values. In fact, if we assume that $ E$ has density one and $ f$ has nonzero order, then the roots of all equations $ f(z) = a$ are equidistributed in angles. In view of a recent result of Murai [6] the conclusions hold in particular for entire functions with Fejér gaps.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1984-0743737-2
PII: S 0002-9947(1984)0743737-2
Article copyright: © Copyright 1984 American Mathematical Society