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2000 Mathematics Subject Classification: Primary 30C10, 30C15, 31B35.
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...
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