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arXiv · 1403.5545

Entire functions with preassigned zero proximate order

A. F. Grishin·Nguyen Van Quynh
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Abstract

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

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A. F. Grishin, Nguyen Van Quynh. 2014-03-21. Entire functions with preassigned zero proximate order. https://arxiv.org/abs/1403.5545

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