Journal ArticleDOI
A Heuristic Principle in Complex Function Theory
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This article is published in American Mathematical Monthly.The article was published on 1975-10-01. It has received 295 citations till now. The article focuses on the topics: Heuristic argument & Heuristic.read more
Citations
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On the singularities of the inverse to a meromorphic function of finite order
TL;DR: In this paper, it was shown that if f is a transcendental meromorphic function, then f with n = 1 takes every finite non-zero value infinitely often, which is a conjecture of Hayman.
Journal ArticleDOI
Normal families: New perspectives
TL;DR: A survey of the application of the Bloch's Principle to one-variable theory can be found in this article, with the aim of making this technique available to as broad an audience as possible.
Journal ArticleDOI
Normal Families and Shared Values
Xuecheng Pang,Lawrence Zalcman +1 more
TL;DR: In this article, a family of meromorphic functions on the plane domain D and a ∈ Copf is defined as a family whose zeros are of multiplicity at least k. The case Ēf(0) = O is a celebrated result.
Book
Basic Complex Analysis
TL;DR: The Cauchy integral theorem and its consequences are discussed in this paper, with a focus on spaces of analytic functions, fractional linear transformations, conformal maps, and elliptic functions.
Journal ArticleDOI
Sharing values and normality
TL;DR: In this article, the authors make an attempt to prove normality criteria using conditions known from sharing value theorems (two meromorphic functions f and g share a e I~ iff f -1 ({a}) = 0 -1 {a}).
References
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BookDOI
Darstellung und Begründung einiger neuerer Ergebnisse der Funktionentheorie
TL;DR: In this paper, acht Kapitel und die Vorgeschichte jener Fragestellungen berichten, im spateren text durchweg vom Einheitskreis die Rede, in dieser Einleitung vom Kreise I x I"
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Correction to: “Inner Product Spaces”
TL;DR: Inner Product Spaces (IPS) as discussed by the authors is a generalization of the concept of product spaces, which is used to describe the inner product spaces of a set of products.