Entire functions with preassigned zero proximate order

DOI10.1007/S10958-015-2523-1zbMath1337.30039arXiv1403.5545OpenAlexW1921340327MaRDI QIDQ906780

A. F. Grishin, Nguen Van Quynh

Publication date: 29 January 2016

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Abstract: It is known that if the proximate order $ho(r)$ such that $limho(r)=ho>0(roinfty)$, then there exists an entire function $f(z)$ of proximate order $ho(r)$. In the case where $ho=0$ the question about the existence of such entire function remained open until now. This question is investigated in the paper.

Full work available at URL: https://arxiv.org/abs/1403.5545

zbMATH Keywords

entire functionproximate orderzero proximate order

Mathematics Subject Classification ID

Entire functions of one complex variable (general theory) (30D20) Special classes of entire functions of one complex variable and growth estimates (30D15)

Cites Work

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• Approximation of subharmonic functions

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