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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the zero sets of certain entire functions

Authors: Alexandre Eremenko and L. A. Rubel
Journal: Proc. Amer. Math. Soc. 124 (1996), 2401-2404
MSC (1991): Primary 30D15
MathSciNet review: 1322920
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Abstract: We consider the class $\mathbf B$ of entire functions of the form

\begin{displaymath}f=\sum p_j\exp g_j,\end{displaymath}

where $p_j$ are polynomials and $g_j$ are entire functions. We prove that the zero-set of such an $f$, if infinite, cannot be contained in a ray. But for every region containing the positive ray there is an example of $f\in \mathbf B$ with infinite zero-set which is contained in this region.

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Additional Information

Alexandre Eremenko
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907

L. A. Rubel
Affiliation: Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801

Received by editor(s): November 14, 1994
Received by editor(s) in revised form: February 7, 1995
Additional Notes: Research supported in part by the National Security Agency
Dedicated: Dedicated in gratitude to the blood donors of Champaign County
Communicated by: Albert Baernstein II
Article copyright: © Copyright 1996 American Mathematical Society