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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Generalization of a theorem of Clunie and Hayman
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by Matthew Barrett and Alexandre Eremenko PDF
Proc. Amer. Math. Soc. 140 (2012), 1397-1402 Request permission

Abstract:

Clunie and Hayman proved that if the spherical derivative $\| f’\|$ of an entire function satisfies $\| f’\|(z)=O(|z|^\sigma )$, then $T(r,f)=O(r^{\sigma +1}).$ We generalize this to holomorphic curves in projective space of dimension $n$ omitting $n$ hyperplanes in general position.
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Additional Information
  • Matthew Barrett
  • Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
  • Alexandre Eremenko
  • Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
  • MR Author ID: 63860
  • Email: eremenko@math.purdue.edu
  • Received by editor(s): November 17, 2010
  • Received by editor(s) in revised form: January 6, 2011
  • Published electronically: August 10, 2011
  • Additional Notes: The first and second authors are supported by NSF grant DMS-0555279
    The second author is also supported by the Humboldt Foundation
  • Communicated by: Mario Bonk
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 140 (2012), 1397-1402
  • MSC (2010): Primary 32Q99, 30D15
  • DOI: https://doi.org/10.1090/S0002-9939-2011-11033-5
  • MathSciNet review: 2869124