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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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Remarks on the Obrechkoff inequality
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by Alexandre Eremenko and Alexander Fryntov PDF
Proc. Amer. Math. Soc. 144 (2016), 703-707 Request permission

Abstract:

Let $u$ be the logarithmic potential of a probability measure $\mu$ in the plane that satisfies \[ u(z)=u(\overline {z}),\quad u(z) \le u(|z|),\quad z\in \mathbb {C},\] and $m(t)=\mu \{ z\in \mathbb {C}^*:|\operatorname {Arg} z|\leq t\}$. Then \[ \frac {1}{a}\int _0^a m(t)dt\leq \frac {a}{2\pi },\] for every $a\in (0,\pi )$. This improves and generalizes a result of Obrechkoff on zeros of polynomials with positive coefficients.
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Additional Information
  • Alexandre Eremenko
  • Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
  • MR Author ID: 63860
  • Alexander Fryntov
  • Affiliation: Physical-Engineering Institute of Low Temperature, National Academy of Sciences of Ukraine, Kharkov 310164, Ukraine
  • MR Author ID: 190280
  • Received by editor(s): November 1, 2014
  • Received by editor(s) in revised form: January 22, 2015, and January 23, 2015
  • Published electronically: August 20, 2015
  • Additional Notes: This work was supported by NSF grant DMS-1361836.
  • Communicated by: Franc Forstneric
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 703-707
  • MSC (2010): Primary 30C15, 31A05
  • DOI: https://doi.org/10.1090/proc/12738
  • MathSciNet review: 3430846