Titlebook: Nevanlinna’s Theory of Value Distribution; The Second Main Theo William Cherry,Zhuan Ye Book 2001 Springer-Verlag Berlin Heidelberg 2001 Co

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ationen und für den technologischen oder prozessualen Fortschritt. Sicher ist, dass die Entwicklung und Entscheidung auf Basis eines minutiös ausgearbeiteten Business-Modells in einer schnelllebigen, volatilen und digitalen Zeit kein vorrangiges Vorgehensmodell mehr sein kann. Denn radikale Innovati

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The Second Main Theorem via Negative Curvature,s [Ahlf 1941]. In Chapter 4, we will give another proof of the Second Main Theorem that is closer to R. Nevanlinna’s original proof. Of course, neither the Nevanlinna brothers nor Ahlfors were interested in the exact structure of the error term. The error term we will present here is essentially due to P.-M. Wong [Wong 1989].

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The Second Main Theorem via Logarithmic Derivatives,s we shall here. A sharp error term in the Second Main Theorem using this type of method was first obtained by Hinkkanen [Hink 1992]. The exact method of proof given here makes use of ideas from Ye’s refinement of Cartan’s method [Cart 1933], as in [Ye 1995].

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Book 2001 terms, in both the geometric and logarithmic derivative based approaches. A unique feature of the monograph is its "number-theoretic digressions". These special sections assume no background in number theory and explore the exciting interconnections between Nevanlinna theory and the theory of Diophantine approximation.

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1439-7382 h is its "number-theoretic digressions". These special sections assume no background in number theory and explore the exciting interconnections between Nevanlinna theory and the theory of Diophantine approximation.978-3-642-08568-0978-3-662-12590-8Series ISSN 1439-7382 Series E-ISSN 2196-9922

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Introduction,na theory, is by saying that the main theorems in value distribution theory are generalizations of the Fundamental Theorem of Algebra to holomorphic and meromorphic functions. The purpose of this book is to describe this theory for meromorphic functions on the complex plane C, or more generally for functions meromorphic in a disc in C.

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Some Applications,ned versions and more detailed exploration of some of the applications we present here. We have, however, also made some limited effort to direct the interested reader to some of the current literature related to the applications discussed here.

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More on the Error Term, by putting rather modest growth restrictions on the functions under consideration and by enlarging the exceptional set, the lower order terms in the error term can be further improved. Finally, in §7.3, we compute the precise form of the error term for some of the more familiar special functions.