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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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

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

  • Dedicated: Dedicated in gratitude to the blood donors of Champaign County
  • 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