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On the self-intersections of the image of the unit circle under a polynomial mapping


Author: J. R. Quine
Journal: Proc. Amer. Math. Soc. 39 (1973), 135-140
MSC: Primary 30A06
DOI: https://doi.org/10.1090/S0002-9939-1973-0313485-X
MathSciNet review: 0313485
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Abstract: We prove that if $ p$ is a polynomial of degree $ n$, then with certain exceptions the image of the unit circle under the mapping $ p$ has at most $ {(n - 1)^2}$ points of self-intersection. We apply our method to the problem of computing polynomials univalent in $ \vert z\vert < 1$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0313485-X
Keywords: Coefficient problem, univalent polynomials, points of self-intersection
Article copyright: © Copyright 1973 American Mathematical Society

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