Results 201 to 210 of about 7,023 (242)

An Introduction to Nevanlinna Theory

1968
The aim of this paper is to give an introduction to R. Nevanlinna’s theory of the distribution of the values assumed by a meromorphic function f(z), perhaps one of the most exciting developments in the function theory of this century. (For a fuller account see my book.5)
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On the Size of the Exceptional Set in Nevanlinna Theory

Journal of the London Mathematical Society, 1986
It is shown an example of a meromorphic function F in the plane, for which the exceptional set in the logarithmic derivative Lemma, in fact occurs. This example generalises a previous construction of Hayman. The function shown is given by a series of the form \[ F(z)=\sum^{\infty}_{n=1}(z/r_ n)^{\lambda_ n}, \] where \(\{r_ n\}\) and \(\{\lambda_ n\}\)
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Nevanlinna theory and iteration of rational maps

Mathematische Zeitschrift, 2004
If \(\varphi \in \mathbb{C}(z)\) is a rational function of degree \(d \geq 2\), then \(\varphi\) defines a holomorphic map \(\mathbb{P}^1(\mathbb{C}) \to \mathbb{P}^1(\mathbb{C})\), where \(\mathbb{P}^1(\mathbb{C})\) is the complex projective space of dimension 1. Let \(\varphi^n\) be the \(n\)-th iterate of \(\varphi\).
Min Ru, Eunjeong Yi
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Nevanlinna Theory of Meromorphic Functions

2014
The value distribution theory of meromorphic functions on C established by R. Nevanlinna in 1925 is described. It not only deepened complex function theory in one variable but also led to the covering theory by L. Ahlfors and the value distribution theory in several complex variables. The aim of this chapter is to introduce the most fundamental part of
Jörg Winkelmann, Junjiro Noguchi, Junjiro Noguchi   +2 more
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Essentials of Nevanlinna Theory

1993
In 1925, R. Nevanlinna[1] established two fundamental theorems; in one stroke he initiated the modern research on the theory of value distribution, and laid down the foundation for its development ever since. Therefore, the first chapter will be devoted to a brief introduction to Nevanlinna theory1), and the last section of the chapter, as an ...
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p-Adic Nevanlinna Theory

2019
After recalling the classical p-adic Nevanlinna theory, we describe the same theory in the complement of an open disk and examine various immediate applications: uniqueness, Picard’s values, branched values, small functions.
Ta Thi Hoai An, Alain Escassut
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Nevanlinna Theory and Minimal Surfaces

1997
In 1915, S. Bernstein proved that there is no nonflat minimal surface in R 3 which is described as the graph of a C 2-function on the total plane R 2 ([9]). This result was improved by many researchers in the field of differential geometry. E. Heinz studied nonflat minimal surfaces in R 3 which are the graph of functions on discs Δ R := {(x, y); x 2 ...
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Nevanlinna Theory and Gap Series

1969
A very attractive feature of complex variable theory is the interplay of the approach via power series (Weierstrass) and the potential theoretical approach (Riemann). The Nevanlinna theory studies the distribution of values of meromorphic functions, by potential-theoretic methods.
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Selected Applications of Nevanlinna Theory

2017
The present chapter is devoted to applications of Nevanlinna Theory to general questions in the theory of entire and meromorphic functions. This concerns algebraic differential and functional equations, uniqueness of meromorphic functions, and the value distribution of differential polynomials. We will always consider meromorphic functions in the plane,
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Equidistribution and Nevanlinna theory

Bulletin of the London Mathematical Society, 2007
Yûsuke Okuyama, David Drasin
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