Migration of zeros for successive derivatives of entire functions
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- by Arie Harel, Su Namn and Jacob Sturm PDF
- Proc. Amer. Math. Soc. 127 (1999), 563-567 Request permission
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.References
- Lars V. Ahlfors, Complex analysis: An introduction of the theory of analytic functions of one complex variable, 2nd ed., McGraw-Hill Book Co., New York-Toronto-London, 1966. MR 0188405
- R. P. Boas Jr. and A. R. Reddy, Zeros of the successive derivatives of entire functions, J. Math. Anal. Appl. 42 (1973), 466–473. Collection of articles dedicated to Salomon Bochner. MR 333183, DOI 10.1016/0022-247X(73)90153-4
- Thomas Craven, George Csordas, and Wayne Smith, The zeros of derivatives of entire functions and the Pólya-Wiman conjecture, Ann. of Math. (2) 125 (1987), no. 2, 405–431. MR 881274, DOI 10.2307/1971315
- M.W. Gontcharoff, Recherches sur les derivees successives des fonctions analytiques, Ann. Sci. de L’Eclole Norm. Sup. Math 47 (1930) pp 1-92.
- Simon Hellerstein and Jack Williamson, Derivatives of entire functions and a question of Pólya, Trans. Amer. Math. Soc. 227 (1977), 227–249. MR 435393, DOI 10.1090/S0002-9947-1977-0435393-4
- Simon Hellerstein and Jack Williamson, Derivatives of entire functions and a question of Pólya. II, Trans. Amer. Math. Soc. 234 (1977), no. 2, 497–503. MR 481004, DOI 10.1090/S0002-9947-1977-0481004-1
- J. J. Corliss, Upper limits to the real roots of a real algebraic equation, Amer. Math. Monthly 46 (1939), 334–338. MR 4
- Herbert S. Wilf, Budan’s theorem for a class of entire functions, Proc. Amer. Math. Soc. 13 (1962), 122–125. MR 133459, DOI 10.1090/S0002-9939-1962-0133459-4
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
- 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
- © Copyright 1999 American Mathematical Society
- 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