On the zero sets of certain entire functions
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- by Alexandre Eremenko and L. A. Rubel
- Proc. Amer. Math. Soc. 124 (1996), 2401-2404
- DOI: https://doi.org/10.1090/S0002-9939-96-03294-7
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Abstract:
We consider the class $\mathbf B$ of entire functions of the form \[ f=\sum p_j\exp g_j,\] 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.References
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Bibliographic Information
- Alexandre Eremenko
- Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
- MR Author ID: 63860
- Email: eremenko@math.purdue.edu
- 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
- Communicated by: Albert Baernstein II
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 2401-2404
- MSC (1991): Primary 30D15
- DOI: https://doi.org/10.1090/S0002-9939-96-03294-7
- MathSciNet review: 1322920
Dedicated: Dedicated in gratitude to the blood donors of Champaign County