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