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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Zeros of derivatives of entire functions
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by Thomas Craven, George Csordas and Wayne Smith PDF
Proc. Amer. Math. Soc. 101 (1987), 323-326 Request permission

Abstract:

It is shown that if a real entire function of genus one has only finitely many nonreal zeros, then, its derivatives, from a certain one onward, have only real zeros.
References
    M. Ålander, Sur le déplacement des zéros des fonctions entières par leur dérivation, dissertation, Upsala, 1914. —, Sur les dérivées successives des fonctions régulières, Opuscula Mathematica A. Wiman Dedicata, Lund, 1930, pp. 79-98.
  • Ralph Philip Boas Jr., Entire functions, Academic Press, Inc., New York, 1954. MR 0068627
  • 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
  • E. Laguerre, Oeuvres, vol. 1, Gauthier-Villars, Paris, 1898. G. Pólya, Über Annäherung durch polynome mit lauter reellen Wurzeln, Rend. Circ. Mat. Palermo 36 (1913), 279-295. —, Some problems connected with Fourier’s work on transcendental equations, Quart. J. Math. Oxford Ser. 1 (1930), 21-34.
  • G. Pólya, Über die Realität der Nullstellen fast aller Ableitungen gewisser ganzer Funktionen, Math. Ann. 114 (1937), no. 1, 622–634 (German). MR 1513163, DOI 10.1007/BF01594201
  • A. Wiman, Über eine asymptotische Eigenschaft der Ableitungen der ganzen Funktionen von den Geschlechtern 1 und 2 mit einer endlichen Anzahl von Nullstellen, Math. Ann. 104 (1931), no. 1, 169–181 (German). MR 1512660, DOI 10.1007/BF01457931
  • A. Wiman, Über die Realität der Nullstellen fast aller Ableitungen gewisser ganzer Funktionen, Math. Ann. 114 (1937), no. 1, 617–621 (German). MR 1513162, DOI 10.1007/BF01594200
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 101 (1987), 323-326
  • MSC: Primary 30D15; Secondary 30C15
  • DOI: https://doi.org/10.1090/S0002-9939-1987-0902550-1
  • MathSciNet review: 902550