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2012 On Sums of Zeros of Infinity Order Entire Functions
M. Gil’
Commun. Math. Anal. 13(1): 100-106 (2012).

Abstract

We consider an infinite order entire functions $f(z)$, whose zeros $z_1(f), z_2(f),\dots$ are enumerated in the increasing order. For a nondecreasing sequence $\{p_k\}$ of positive numbers, a bound for the sums $$ \sum_{k=1}^j \frac{1}{|z_k(f)|^{p_k}}\;\;(j=1, 2,\dots) $$ is suggested. That bound gives us conditions providing the convergence of the corresponding series.

Citation

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M. Gil’. "On Sums of Zeros of Infinity Order Entire Functions." Commun. Math. Anal. 13 (1) 100 - 106, 2012.

Information

Published: 2012
First available in Project Euclid: 2 October 2012

zbMATH: 1346.30013
MathSciNet: MR2998350

Subjects:
Primary: 30D20

Rights: Copyright © 2012 Mathematical Research Publishers

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Vol.13 • No. 1 • 2012
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