On the zeros of entire functions with a majorant of infinite order

Bykov, S.; Shamoyan, F.

doi:10.1090/S1061-0022-2010-01124-5

On the zeros of entire functions with a majorant of infinite order
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by S. V. Bykov and F. A. Shamoyan
Translated by: A. Plotkin

St. Petersburg Math. J. 21 (2010), 893-901

DOI: https://doi.org/10.1090/S1061-0022-2010-01124-5

Published electronically: September 22, 2010

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Abstract:

The class of entire functions $f$ satisfying $\ln |f(z)|\le C_f\lambda (|z|)$, $z\in \mathbb {C}$, where $\lambda$ is a majorant mentioned in the title, admits a zero set $\{z_j\}$ such that $\{|z_j|\}$ is a uniqueness set for this class.

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