Angular distribution in complex oscillation theory

Wu, Shengjian

doi:10.1360/03ys0159

Cited by 7 publications

(7 citation statements)

References 6 publications

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“…Some new singular directions were introduced by several researchers, such as Hayman direction, T direction, and Hayman-T direction, see [26,29,8,31]. In 2005, Wu [23] first studied the Borel directions of solutions of second order linear differential equations. The general form of such equations is given by…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

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The radial oscillation of entire solutions of complex differential equations

Huang

Wang

2015

Journal of Mathematical Analysis and Applications

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Section: Introduction and Main Resultsmentioning

confidence: 99%

“…However, the research on the properties of solutions in an angle is not so active. Indeed, Wu [23] consider (1) with B(z) ≡ F (z) ≡ 0. For the product of a solution base, he found the connection of the radial exponent of convergence of zeros with Borel directions.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

The radial oscillation of entire solutions of complex differential equations

Huang

Wang

2015

Journal of Mathematical Analysis and Applications

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“…Recently, Wu [18] proved the following theorem on connection of the radial exponent of convergence of zeros with Borel direction of the product of a solution base of (1).…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Radial Oscillation of Linear Differential Equation

Wu¹

2012

Bulletin of the Korean Mathematical Society

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“…The inequality (2.4.8) with (1) was attained by Zhang X. L. [40] and (2.4.8) with (2) by the author [41] in a different way from that of Zhang [40] under the assumption that T (r, Ω ) > (log r) p , p > 2. The inequality (2.4.8) with (1) was attained by Zhang X. L. [40] and (2.4.8) with (2) by the author [41] in a different way from that of Zhang [40] under the assumption that T (r, Ω ) > (log r) p , p > 2.…”

Section: Theorem 243mentioning

confidence: 98%

“…The present author in [42] suggested first time to investigate uniqueness of a meromorphic function in a precise subset ofĈ, that is, Question 2.9.1 for X = C, and believes this would be an interesting topic. A number of unique theorems in angular domains were established in Zheng [42] and [43] in terms of Nevanlinna characteristic for angular domains.…”

Section: Uniqueness Of Meromorphic Functions Related To Some Angular mentioning

confidence: 99%

Value Distribution of Meromorphic Functions

Zheng¹

2011

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The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: Frido Steinen-Broo, EStudio Calamar, SpainPrinted on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) Preface This book is devoted to the study of value distribution of functions which are meromorphic on the complex plane or in an angular domain with vertex at the origin. We characterize such meromorphic functions in terms of distribution of some of their value points. The study, together with certain related topics, is known as theory of value distribution of meromorphic functions. The theory is too vast to be justified within a single work. Therefore we selected and organized the content based on their significant importance to our understanding and interests in this book. I gladly acknowledge my indebtedness in particular to the books of M. Tsuji, A. A. Goldberg and I. V. Ostrovskii, Yang L. and the papers of A. Eremenko.An outline of the book is provided below. The introduction of the Nevanlinna characteristic to the study of meromorphic functions is a new starting symbol of the theory of value distribution. The Nevanlinna characteristic is powerful, and its thought has been used to produce various characteristics such as the Nevanlinna characteristic and Tsuji characteristic for an angular domain. And from geometric point of view, namely the Ahlfors theory of covering surfaces, the Ahlfors-Shimizu characteristic have also been introduced. These characteristics are real-valued functions defined on the positive real axis. Therefore, in the first chapter, we collect the basic results about positive real functions that are often used in the study of meromorphic function theory. Some of these results are distributed in other books, some in published papers, and some have been newly established in order to serve our specific objectives in the book.In the present book, we discuss value distribution not only in the complex plane, but also in an angular domain. Therefore, we introduce, in the second chapter, various characteristics of a meromorphic function: The Nevanlinna characteristic for a disk, the Nevanlinna characteristic for an angle, the Tsuji characteristic and the Ahlfors-Shimizu characteristic for an angle. Although they were distributed in another books, we collected all of them, and more importantly, we carefully compared them with one another to reveal their relations that enabled us to produce new results and applications. We establish the first and second fundamental theorems for the various characteristics and the corresponding integrated counting functions, and provide an estimate of the error term related to the Nevanlinna characteristic for an ii Preface angle in terms of the Nevanlinna characteristic in a larger angle. We discuss in an angle the growth order of a meromorphic func...

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Angular distribution in complex oscillation theory

Cited by 7 publications

References 6 publications

The radial oscillation of entire solutions of complex differential equations

The radial oscillation of entire solutions of complex differential equations

Radial Oscillation of Linear Differential Equation

Value Distribution of Meromorphic Functions

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