SOME MORE COUNTEREXAMPLES FOR BOMBIERI'S CONJECTURE ON UNIVALENT FUNCTIONS

被引：0

作者：

Efraimidis, Iason ^{[1
]}

Pastor, Carlos ^{[2
]}

机构：

[1] Pontificia Univ Catolica Chile, Fac Matemat, Ave Vicuna Mackenna 4860, Santiago, Chile

[2] Inst Ciencias Matemat, Nicolas Cabrera 13-15, Madrid 28049, Spain

来源：

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY | 2018年 / 55卷 / 06期

关键词：

univalent functions; Bombieri conjecture; trigonometric inequalities;

D O I：

10.4134/JKMS.j170779

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 >= 2 when m is odd and n is even, m is sufficiently big and 0.5 <= n/m <= 0.8194.

引用

页码：1485 / 1498

页数：14

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