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Brown, Johnny E.; Xiang, Guangping Proof of the Sendov conjecture for polynomials of degree at most eight.
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of the roots. It follows that the critical points must be within the unit disk, since the roots are.
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Problem 4.5, W. K. Hayman, Research
Problems in Function Theory. Althlone Press, London, 1967.
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Terence Tao (2020). "Sendov's conjecture for sufficiently high degree polynomials".
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roots is at a distance no more than 1 from at least one critical point.
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Marden, Morris. Conjectures on the
Critical Points of a Polynomial.
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397:"Sendov's conjecture for sufficiently high degree polynomials"
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Approximation Theory: A Volume
Dedicated to Blagovest Sendov
345:< 8 in 1996. Brown and Xiang proved the conjecture for
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by Bruce
Torrence with contributions from Paul Abbott at
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in 1959; he described the conjecture to his colleague
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says that all of the critical points lie within the
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50:The conjecture states that for a polynomial
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16:Conjecture about the roots of polynomials
196:The conjecture has been proven for
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341:< 7. Borcea extended the proof to
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466:Sendov's Conjecture
187:Gauss–Lucas theorem
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25:Ilieff's conjecture
21:Sendov's conjecture
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