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On the zero sets of certain entire functions |
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| Authors: | Alexandre Eremenko L. A. Rubel |
| Affiliation: | Department of Mathematics, Purdue University, West Lafayette, Indiana 47907 ; Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801 |
| Abstract: | We consider the class  of entire functions of the form
where |
| Keywords: | |
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are polynomials and 
are entire functions. We prove that the zero-set of such an 
, if infinite, cannot be contained in a ray. But for every region containing the positive ray there is an example of 
with infinite zero-set which is contained in this region.