Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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SOME MORE COUNTEREXAMPLES FOR BOMBIERI'S CONJECTURE ON UNIVALENT FUNCTIONS

  • Received : 2017.12.05
  • Accepted : 2018.03.27
  • Published : 2018.11.01
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Abstract

We disprove a conjecture of Bombieri regarding univalent functions in the unit disk in some previously unknown cases. The key step in the argument is showing that the global minimum of the real function (n sin x - sin(nx))/(m sin x - sin(mx)) is attained at x = 0 for integers m > $n{\geq}2$ when m is odd and n is even, m is sufficiently big and $0.5{\leq}n/m{\leq}0.8194$.

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References

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