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Value Distribution of Meromorphic Functions
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A survey of results after 1970 can be found in this paper, where the authors present a survey of meromorphic functions of finite-order functions with respect to Riemann surfaces.Abstract:
Characteristics of the behavior of a meromorphic function and the first fundamental theorem Meromorphic functions of finite order The second fundamental theorem Deficient values Asymptotic properties of meromorphic functions and deficiencies Value distribution with respect to the arguments Applications of Riemann surfaces to value distribution On the magnitude of an entire function Notes A survey of some results after 1970 Bibliography References added to the English edition Author index Subject index Notation index.read more
Citations
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Theory of Functions of a Complex Variable
TL;DR: The theory of functions is the basis on which the whole of pure mathematics which deals with continuously varying quantity rests as mentioned in this paper, and the answer would not be too wide nor would it always imply too much.
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Holomorphic curves with shift-invariant hyperplane preimages
TL;DR: In this article, a difference analogue of M. Green's Picard-type theorem for holomorphic curves is presented, which can be described as a difference analog of Green's first main theorem for the Casorati determinant and an extended version of the difference analogue on the logarithmic derivatives.
Journal ArticleDOI
Value sharing results for shifts of meromorphic functions, and sufficient conditions for periodicity
TL;DR: In this paper, it was shown that if a meromorphic function f (z ) is of finite order and shares two values CM and one value IM with its shift f ( z + c ), then f is a periodic function with period c. The assumption on the order of f can be dropped if f shares two shifts in different directions, leading to a new way of characterizing elliptic functions.
Journal ArticleDOI
Constructing entire functions by quasiconformal folding
TL;DR: In this paper, the authors give a method for constructing transcendental entire functions with good control of both the singular values of f and the geometry of f. Among other applications, they construct a function f with bounded singular set, whose Fatou set contains a wandering domain.
Book ChapterDOI
Diophantine Approximation and Nevanlinna Theory
TL;DR: It has been known that the branch of complex analysis known as Nevanlinna theory (also called value distribution theory) has many similarities with Roth's theorem on diophantine approximation.
References
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Iteration of meromorphic functions
TL;DR: In this paper, the authors describe some of the results obtained in the iteration theory of transcendental meromorphic functions, not excluding the case of entire functions, and some aspects where the transcendental case is analogous to the rational case are treated rather briefly here.
Book
A course of modern analysis; an introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions
TL;DR: The theory of Riemann integration as mentioned in this paper is a generalization of the theory of complex numbers, and it can be expressed as follows: 1. Complex numbers 2. The theory of convergence 3. Continuous functions and uniform convergence 4. The fundamental properties of analytic functions 5. The expansion of functions in infinite series 6.