# Smale's Conjecture on Mean Values of Polynomials and Electrostatics

Serdica Mathematical Journal (2007)

- Volume: 33, Issue: 4, page 399-410
- ISSN: 1310-6600

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topDimitrov, Dimitar. "Smale's Conjecture on Mean Values of Polynomials and Electrostatics." Serdica Mathematical Journal 33.4 (2007): 399-410. <http://eudml.org/doc/281352>.

@article{Dimitrov2007,

abstract = {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 the electrostatic
equilibrium related to polynomials with zeros in a ring domain is formulated
and discussed.Research supported by the Brazilian foudations CNPq under Grant 304830/2006-2 and
FAPESP under Grant 03/01874-2.},

author = {Dimitrov, Dimitar},

journal = {Serdica Mathematical Journal},

keywords = {Zeros of Polynomials; Critical Points; Smale’s Conjecture; Extremal Problem; Electrostatics; zeros of polynomials; critical points; Smale's conjecture; extremal problem; electrostatics},

language = {eng},

number = {4},

pages = {399-410},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {Smale's Conjecture on Mean Values of Polynomials and Electrostatics},

url = {http://eudml.org/doc/281352},

volume = {33},

year = {2007},

}

TY - JOUR

AU - Dimitrov, Dimitar

TI - Smale's Conjecture on Mean Values of Polynomials and Electrostatics

JO - Serdica Mathematical Journal

PY - 2007

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 33

IS - 4

SP - 399

EP - 410

AB - 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 the electrostatic
equilibrium related to polynomials with zeros in a ring domain is formulated
and discussed.Research supported by the Brazilian foudations CNPq under Grant 304830/2006-2 and
FAPESP under Grant 03/01874-2.

LA - eng

KW - Zeros of Polynomials; Critical Points; Smale’s Conjecture; Extremal Problem; Electrostatics; zeros of polynomials; critical points; Smale's conjecture; extremal problem; electrostatics

UR - http://eudml.org/doc/281352

ER -

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