Zeros of Polynomials Critical Points Smale’s Conjecture Extremal Problem Electrostatics
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.
