[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.j170779

SOME MORE COUNTEREXAMPLES FOR BOMBIERI'S CONJECTURE ON UNIVALENT FUNCTIONS

Efraimidis, Iason (Facultad de Matematicas Pontificia Universidad Catolica de Chile)
Pastor, Carlos (Instituto de Ciencias Matematicas)

Publication Information

Journal of the Korean Mathematical Society / v.55, no.6, 2018 , pp. 1485-1498 More about this Journal

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 $0.5{\leq}n/m{\leq}0.8194$ .

Keywords

univalent functions; Bombieri conjecture; trigonometric inequalities;

Citations & Related Records

Reference

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