Critical points of real entire functions and a conjecture of Pólya
Author:
YoungOne Kim
Journal:
Proc. Amer. Math. Soc. 124 (1996), 819830
MSC (1991):
Primary 30D15, 30D35
MathSciNet review:
1301508
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Abstract: Let be a nonconstant real entire function of genus and assume that all the zeros of are distributed in some infinite strip , . It is shown that (1) if has nonreal zeros in the region , and has nonreal zeros in the same region, and if the points and are located outside the Jensen disks of , then has exactly critical zeros in the closed interval , (2) if is at most of order , , and minimal type, then for each positive constant there is a positive integer such that for all has only real zeros in the region , and (3) if is of order less than , then has just as many critical points as couples of nonreal zeros.
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Additional Information
YoungOne Kim
Affiliation:
Department of Mathematics, College of Natural Sciences, Sejong University, Seoul 133–747, Korea
DOI:
http://dx.doi.org/10.1090/S0002993996030833
PII:
S 00029939(96)030833
Keywords:
P\'{o}lyaWiman conjecture,
LaguerreP\'{o}lya class,
Fourier critical point
Received by editor(s):
March 28, 1994
Received by editor(s) in revised form:
September 7, 1994
Additional Notes:
This research is supported by the research grant of the Ministry of Education, Republic of Korea, and SNU–GARC.
Dedicated:
To the memory of Professor Jongsik Kim
Communicated by:
Albert Baernstein II
Article copyright:
© Copyright 1996 American Mathematical Society
