Continuous independence and the Ilieff-Sendov conjecture
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- by Michael J. Miller PDF
- Proc. Amer. Math. Soc. 115 (1992), 79-83 Request permission
Abstract:
A maximal polynomial is a complex polynomial that has all of its roots in the unit disk, one fixed root, and all of its critical points as far as possible from a fixed point. In this paper we determine a lower bound for the number of roots and critical points of a maximal polynomial that must lie on specified circles.References
- Johnny E. Brown, On the Ilieff-Sendov conjecture, Pacific J. Math. 135 (1988), no. 2, 223–232. MR 968610
- A. W. Goodman, Q. I. Rahman, and J. S. Ratti, On the zeros of a polynomial and its derivative, Proc. Amer. Math. Soc. 21 (1969), 273–274. MR 239062, DOI 10.1090/S0002-9939-1969-0239062-6 F. Hohn, Introduction to linear algebra, Macmillan, New York, 1972.
- Morris Marden, Geometry of polynomials, 2nd ed., Mathematical Surveys, No. 3, American Mathematical Society, Providence, R.I., 1966. MR 0225972
- Morris Marden, Conjectures on the critical points of a polynomial, Amer. Math. Monthly 90 (1983), no. 4, 267–276. MR 700266, DOI 10.2307/2975758
- Michael J. Miller, Maximal polynomials and the Ilieff-Sendov conjecture, Trans. Amer. Math. Soc. 321 (1990), no. 1, 285–303. MR 965744, DOI 10.1090/S0002-9947-1990-0965744-X
- Gerhard Schmeisser, Bemerkungen zu einer Vermutung von Ilieff, Math. Z. 111 (1969), 121–125 (German). MR 264040, DOI 10.1007/BF01111192
Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 115 (1992), 79-83
- MSC: Primary 30C15
- DOI: https://doi.org/10.1090/S0002-9939-1992-1113647-X
- MathSciNet review: 1113647