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On the Ilieff-Sendov
conjecture
Johnny E. Brown |
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Vol. 135 (1988), No. 2, 223–232
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Abstract |
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The well-known Ilieff-Sendov conjecture asserts that for any polynomial p(z) = XTk=l{z−zk) with ∖zk∖← 1, each of the disks. ∖z − zk∖≤ 1 (1 ≤ k ≤ n) must contain a critical point of p. This conjecture is proved for polynomials of arbitrary degree n with at most four distinct zeros. This extends a result of Saff and Twomey. |
Mathematical Subject Classification 2000
Primary: 30C15
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Milestones
Received: 9 June 1987
Published: 1 December 1988
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Authors |
| Johnny E. Brown | |
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