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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Migration of zeros for successive derivatives
of entire functions


Authors: Arie Harel, Su Namn and Jacob Sturm
Journal: Proc. Amer. Math. Soc. 127 (1999), 563-567
MSC (1991): Primary 30A66
MathSciNet review: 1468192
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Abstract: It is shown that if $f$ is an entire function of order less than one, all of whose zeros are real, then the minimal root of $f^{(k)}$ is an increasing function of $k$ which accelerates as $k$ increases.


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Additional Information

Arie Harel
Affiliation: Department of Mathematics, National University of Singapore, Lower Kent Ridge Road, Singapore 119260
Email: harel@math.nus.edu.sg

Su Namn
Affiliation: Department of Management Information Systems, Hannam University, Taejon, Korea
Email: namn@eve.hannam.ac.kr

Jacob Sturm
Affiliation: Department of Mathematics and Computer Science, Rutgers University, Newark, New Jersey 07102
Email: sturm@andromeda.rutgers.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04542-6
PII: S 0002-9939(99)04542-6
Keywords: Successive derivatives, entire functions, migration
Received by editor(s): December 29, 1996
Received by editor(s) in revised form: March 24, 1997, and June 4, 1997
Communicated by: Albert Baernstein II
Article copyright: © Copyright 1999 American Mathematical Society