论文标题
Erdös最大模量点问题的大概解决方案
An approximate solution to Erdös' maximum modulus points problem
论文作者
论文摘要
在本说明中，我们研究了整个功能的最大模量点数量的渐近行为，位于半径$ r $的光盘中。 1964年，Erd \ humlaut {o}询问是否存在非公主函数，以使该数量无限？倾向于无限？ 1968年，赫尔佐格（Herzog）和皮拉尼亚人（Piranian）建造了一张无限制的地图。然而，今天仍然尚不清楚它是否有可能无限。在本文中，我们构建了一个任意接近满足此财产的先验整个功能，从而提供了支持该问题积极答案的最有力的证据。
In this note we investigate the asymptotic behavior of the number of maximum modulus points, of an entire function, sitting in a disc of radius $r$. In 1964, Erd\Humlaut{o}s asked whether there exists a non-monomial function so that this quantity is unbounded? tends to infinity? In 1968 Herzog and Piranian constructed an entire map for which it is unbounded. Nevertheless, it is still unknown today whether it is possible that it tends to infinity or not. In this paper, we construct a transcendental entire function that is arbitrarily close to satisfying this property, thereby giving the strongest evidence supporting a positive answer to this question.
