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Titlebook: Value Distribution Theory; Yang Lo Book 1993 Springer-Verlag Berlin Heidelberg 1993 Meromorphe Funktionen.Meromorphic function.Nevanlinna

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發(fā)表于 2025-3-21 16:25:07 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Value Distribution Theory
編輯Yang Lo
視頻videohttp://file.papertrans.cn/981/980336/980336.mp4
圖書封面Titlebook: Value Distribution Theory;  Yang Lo Book 1993 Springer-Verlag Berlin Heidelberg 1993 Meromorphe Funktionen.Meromorphic function.Nevanlinna
描述It is well known that solving certain theoretical or practical problems often depends on exploring the behavior of the roots of an equation such as (1) J(z) = a, where J(z) is an entire or meromorphic function and a is a complex value. It is especially important to investigate the number n(r, J = a) of the roots of (1) and their distribution in a disk Izl ~ r, each root being counted with its multiplicity. It was the research on such topics that raised the curtain on the theory of value distribution of entire or meromorphic functions. In the last century, the famous mathematician E. Picard obtained the pathbreaking result: Any non-constant entire function J(z) must take every finite complex value infinitely many times, with at most one excep- tion. Later, E. Borel, by introducing the concept of the order of an entire function, gave the above result a more precise formulation as follows. An entire function J (z) of order A( 0 < A < (0) satisfies -1‘ logn(r, J = a) 1m = 1 r->oo logr for every finite complex value a, with at most one exception. This result, generally known as the Picard-Borel theorem, lay the foundation for the theory of value distribution and since then has been the
出版日期Book 1993
關(guān)鍵詞Meromorphe Funktionen; Meromorphic function; Nevanlinna theory; Value Distribution; Werteverteilung; deri
版次1
doihttps://doi.org/10.1007/978-3-662-02915-2
isbn_softcover978-3-662-02917-6
isbn_ebook978-3-662-02915-2
copyrightSpringer-Verlag Berlin Heidelberg 1993
The information of publication is updating

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沙發(fā)
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板凳
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Essentials of Nevanlinna Theory,laid down the foundation for its development ever since. Therefore, the first chapter will be devoted to a brief introduction to Nevanlinna theory., and the last section of the chapter, as an illustration of the development, will discuss an important theorem by Osgood. and Steinmetz..
地板
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Normal Families,ed to that of the properties of a family of functions in a fixed region. For this purpose, an introduction to the concept of normal family and some criteria for normality would be appropriate. Nevanlinna theory plays an important role in this discussion.
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發(fā)表于 2025-3-22 08:51:49 | 只看該作者
Borel Directions,ng the theory of normal family, investigations were made into the behavior of an entire or meromorphic function near a ray by H. Milloux “filling disks” [1], A. Ostrowski [1], and others. This fieled of study is refered to as angular distribution theory. In 1928, starting from Nevanlinna theory, G.
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Deficient Values and Borel Directions of Meromorphic Functions,ar distribution theory, where the definition of a deficient value depends only on the modulii of the points at which the function takes on this value. It would therefore not appear initially to be the case that there is any relationship between Borel directions and deficient values. However, Yang Lo
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發(fā)表于 2025-3-22 18:32:18 | 只看該作者
Book 1993) J(z) = a, where J(z) is an entire or meromorphic function and a is a complex value. It is especially important to investigate the number n(r, J = a) of the roots of (1) and their distribution in a disk Izl ~ r, each root being counted with its multiplicity. It was the research on such topics that
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發(fā)表于 2025-3-23 00:12:07 | 只看該作者
Deficient Values and Borel Directions of Meromorphic Functions, and Zhang Guanghou have shown that if a meromorphic function of finite positive order has a deficient value, then the distribution of its Borel directions has to follow a certain rule. In the general case, the deficient values and Borel directions are closely related to each other in number.
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ts of offshore production activities. It took nearly five years to complete and involved almost 30 individual research groups. All of the raw data have been archived with NOAA‘s Environmental Data and Information Services, and detailed technical reports have been deposited with the National Technica
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