BulDML at Institute of Mathematics and Informatics >
IMI Periodicals >
Serdica Mathematical Journal >
2007 >
Volume 33, Number 4 >

Please use this identifier to cite or link to this item:

Title: Smale's Conjecture on Mean Values of Polynomials and Electrostatics
Authors: Dimitrov, Dimitar
Keywords: Zeros of Polynomials
Critical Points
Smale’s Conjecture
Extremal Problem
Issue Date: 2007
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 33, No 4, (2007), 399p-410p
Abstract: A challenging conjecture of Stephen Smale on geometry of polynomials is under discussion. We consider an interpretation which turns out to be an interesting problem on equilibrium of an electrostatic field that obeys the law of the logarithmic potential. This interplay allows us to study the quantities that appear in Smale’s conjecture for polynomials whose zeros belong to certain specific regions. A conjecture concerning the electrostatic equilibrium related to polynomials with zeros in a ring domain is formulated and discussed.
Description: 2000 Mathematics Subject Classification: Primary 30C10, 30C15, 31B35.
ISSN: 1310-6600
Appears in Collections:Volume 33, Number 4

Files in This Item:

File Description SizeFormat
2007-399-410.pdf440.54 kBAdobe PDFView/Open


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.


Valid XHTML 1.0!   Creative Commons License