The growth irregularity of slowly growing entire functions
Ostrovskii, I. V.
Üreyen, A. E.
Functional Analysis and its Applications
Springer New York LLC
304 - 312
Item Usage Stats
MetadataShow full item record
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.
KeywordsClunie - Kövari theorem
Erdös - Kövari theorem
Hayman convexity theorem
Levin ' s strong proximate order