Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 30D15

Retrieve articles in all journals with MSC (1991): 30D15

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

PII: S 0002-9939(96)03294-7
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

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia