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

DOI:
https://doi.org/10.1090/S0002-9939-99-04542-6

MathSciNet review:
1468192

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Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that if is an entire function of order less than one, all of whose zeros are real, then the minimal root of is an increasing function of which accelerates as increases.

**[A]**L. Ahlfors,*Complex Analysis: An introduction to the theory of analytic functions of one complex variable*, McGraw-Hill, (1966). MR**32:5844****[B]**R.P. Boas, Jr.,*Zeros of the successive derivates of entire functions*, J. of Math. Analysis and Applications**42**(1973), 446-473. MR**48:11508****[CCS]**T. Craven, G. Csordas and W. Smith,*The zeros of derivatives of entire functions and the Pólya-Wiman Conjecture*, Ann. of Math.**125**(1987), 405-431. MR**88a:30007****[G]**M.W. Gontcharoff,*Recherches sur les derivees successives des fonctions analytiques*, Ann. Sci. de L'Eclole Norm. Sup. Math**47**(1930) pp 1-92.**[HW1]**S. Hellerstein and J. Williamson,*Derivatives of entire functions and a question of Pólya*, Trans. of the Amer. Math. Soc.**227**(1977), 227-249. MR**55:8353****[HW2]**S. Hellerstein and J. Williamson,*Derivatives of entire functions and a question of Pólya II*, Trans. of the Amer. Math. Soc.**234**(1977), 497-503. MR**58:1151****[P]**G. Pólya,*On the zeros of the derivatives of a function and its analytic character*, Bull. Amer. Math. Soc**49**(1943), 178-191. MR**4:192d****[W]**M. S. Wilf,*Budan's theorem for a class of entire functions*, Proc. Amer. Math. Soc.**13**(1962), 122-125. MR**24:A3290**

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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:
https://doi.org/10.1090/S0002-9939-99-04542-6

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