On Bloch’s “Principle of Topological Continuity”

IF 0.6 4区数学 Q3 MATHEMATICS

Computational Methods and Function Theory Pub Date : 2024-04-04 DOI:10.1007/s40315-024-00531-w

Walter Bergweiler, Alexandre Eremenko

引用次数: 0

Abstract

We discuss to what extent certain results about totally ramified values of entire and meromorphic functions remain valid if one relaxes the hypothesis that some value is totally ramified by assuming only that all islands over some Jordan domain are multiple. In particular, we prove a result suggested by Bloch which says that an entire function of order less than 1 has a simple island over at least one of two given Jordan domains with disjoint closures.

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论布洛赫的 "拓扑连续性原理"

我们讨论了如果只假定某个约旦域上的所有岛都是多重的，从而放宽某些值是完全夯实的这一假设，那么关于全函数和分形函数的完全夯实值的某些结果在多大程度上仍然有效。特别是，我们证明了布洛赫提出的一个结果，即一个阶小于 1 的全函数在两个给定的约旦域中至少有一个具有不相交的闭合域上有一个简单岛。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computational Methods and Function Theory MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.20

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： CMFT is an international mathematics journal which publishes carefully selected original research papers in complex analysis (in a broad sense), and on applications or computational methods related to complex analysis. Survey articles of high standard and current interest can be considered for publication as well.