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Dual Smale's mean value conjecture


Authors: Aimo Hinkkanen, Ilgiz R. Kayumov and Diana M. Khammatova
Journal: Proc. Amer. Math. Soc. 147 (2019), 5227-5237
MSC (2010): Primary 30C10
DOI: https://doi.org/10.1090/proc/14639
Published electronically: July 8, 2019
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Abstract: We prove the dual Smale's mean value conjecture for polynomials of degree six: if $ f$ is a polynomial of degree six with $ f(0)=0$ and $ f'(0)=1$, then there is a point $ \zeta $ such that $ f'(\zeta )=0 $ and $ \vert f(\zeta )/\zeta \vert \geq 1/6$.


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Additional Information

Aimo Hinkkanen
Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, Illinois 61801-2975
Email: aimo@math.uiuc.edu

Ilgiz R. Kayumov
Affiliation: Kazan Federal University, Kremlevskaya 18, 420 008 Kazan, Russia
Email: ikayumov@kpfu.ru

Diana M. Khammatova
Affiliation: Kazan Federal University, Kremlevskaya 18, 420 008 Kazan, Russia
Email: dianalynx@rambler.ru

DOI: https://doi.org/10.1090/proc/14639
Received by editor(s): May 28, 2017
Received by editor(s) in revised form: December 21, 2018, and March 6, 2019
Published electronically: July 8, 2019
Additional Notes: The research of the second and third authors was funded by the subsidy allocated to Kazan Federal University for the state assignment in the sphere of scientific activities, project no. 1.13556.2019/13.1.
Communicated by: Jeremy Tyson
Article copyright: © Copyright 2019 American Mathematical Society