The growth irregularity of slowly growing entire functions

Date

2006

Authors

Ostrovskii, I. V.
Üreyen, A. E.

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Abstract

We show that entire transcendental functions f satisfying log M(r,f) = o(log 2r), r → ∞ (M(r,f): = maxf(z)| necessarily have growth irregularity, which increases as the growth diminishes. In particular, if 1 < p < 2, then the asymptotics log M(r,f) = (log pr) +0 (log2-pr), r → ∞ is impossible. It becomes possible if "o" is replaced by "O.". © Springer Science+Business Media, Inc. 2006.

Source Title

Functional Analysis and its Applications

Publisher

Springer New York LLC

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Published Version (Please cite this version)

Language

English