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Funktsional'nyi Analiz i ego Prilozheniya, 2006, Volume 40, Issue 4, Pages 72–82
DOI: https://doi.org/10.4213/faa851 (Mi faa851) 		 
This article is cited in 1 scientific paper (total in 1 paper)

The Growth Irregularity of Slowly Growing Entire Functions

I. V. Ostrovskiiab, A. E. Üreyenb

a B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine
b Bilkent University
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DOI: https://doi.org/10.4213/faa851
Abstract: We show that entire transcendental functions $f$ satisfying
$$ \log M(r,f)=o(\log^2r),\qquad r\to\infty\quad (M(r,f):=\max_{|z|=r}|f(z)|) $$
necessarily have growth irregularity, which increases as the growth diminishes. In particular, if $1<p<2$, then the asymptotics
$$ \log M(r,f)=\log^pr+o(\log^{2-p}r),\qquad r\to\infty, $$
is impossible. It becomes possible if "$o$" is replaced by "$O$."
Keywords: Clunie–Kövari theorem, Erdös–Kövari theorem, Hayman convexity theorem, maximum term, Levin's strong proximate order.
Received: 15.03.2006
English version:
Functional Analysis and Its Applications, 2006, Volume 40, Issue 4, Pages 304–312
DOI: https://doi.org/10.1007/s10688-006-0047-7
Bibliographic databases:
Document Type: Article
UDC: 517.53
Language: Russian
Citation: I. V. Ostrovskii, A. E. Üreyen, “The Growth Irregularity of Slowly Growing Entire Functions”, Funktsional. Anal. i Prilozhen., 40:4 (2006), 72–82; Funct. Anal. Appl., 40:4 (2006), 304–312
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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