A bound for Smale's mean value conjecture for complex polynomials

Research output: Contribution to journalArticle (Academic Journal)peer-review

8 Citations (Scopus)

Abstract

Smale's mean value conjecture is an inequality that relates the locations of critcal points and critical avalues of a polynomial p to the value and derivative of p at some given non-critical point. Using known estimatates for the logarithmic capacity of a connected set in the plane containing three given points, we give a new bound for the constant in Smale's inequality in terms of the degree d of p. The bound improves previous results when d > 8.
Translated title of the contributionA bound for Smale's mean value conjecture for complex polynomials
Original languageEnglish
Pages (from-to)781 - 791
Number of pages11
JournalBulletin of the London Mathematical Society
Volume39 (5)
DOIs
Publication statusPublished - Oct 2007

Bibliographical note

Publisher: Oxford University Press

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