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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 

 

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


Authors: S. V. Bykov and F. A. Shamoyan
Translated by: A. Plotkin
Original publication: Algebra i Analiz, tom 21 (2009), nomer 6.
Journal: St. Petersburg Math. J. 21 (2010), 893-901
MSC (2010): Primary 30D15
DOI: https://doi.org/10.1090/S1061-0022-2010-01124-5
Published electronically: September 22, 2010
MathSciNet review: 2604543
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Abstract: The class of entire functions $ f$ satisfying $ \ln \vert f(z)\vert\le C_f\lambda (\vert z\vert)$, $ z\in \mathbb{C}$, where $ \lambda$ is a majorant mentioned in the title, admits a zero set $ \{z_j\}$ such that $ \{\vert z_j\vert\}$ is a uniqueness set for this class.


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Additional Information

S. V. Bykov
Affiliation: Bryansk State University, 14 Bezhitskaya Street, Bryansk 241036, Russia
Email: b_serecha@mail.ru

F. A. Shamoyan
Affiliation: Bryansk State University, 14 Bezhitskaya Street, Bryansk 241036, Russia
Email: shamoyanfa@yandex.ru

DOI: https://doi.org/10.1090/S1061-0022-2010-01124-5
Keywords: Entire function, Lindelöf condition, zero set
Received by editor(s): April 15, 2008
Published electronically: September 22, 2010
Additional Notes: Supported by RFBR (grant no. 09-01-97517).
Dedicated: To our Teacher Viktor Petrovich Havin on the occasion of his 75th birthday
Article copyright: © Copyright 2010 American Mathematical Society