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The Gauss–Lucas theorem in an asymptotic sense
Author(s) -
Totik Vilmos
Publication year - 2016
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdw047
Subject(s) - mathematics , gauss , sense (electronics) , calculus (dental) , medicine , electrical engineering , physics , dentistry , quantum mechanics , engineering
According to the Gauss–Lucas theorem, if all zeros of a polynomial lie in a convex set K , then all zeros of its derivative also lie in K . In this paper, it is shown that if almost all zeros of polynomials lie in a convex set K , then almost all zeros of their derivatives lie in any fixed neighborhood of K .
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