Chung-Chun Yang

Uniqueness theory of meromorphic functions

1 Basic Nevanlinna theory.- 2 Unicity of functions of finite (lower) order.- 3 Five-value, multiple value and uniqueness.- 4 The four-value theorem.- 5 Functions sharing three common values.- 6 Three-value sets of meromorphic functions.- 7 Functions sharing one or two values.- 8 Functions sharing values with their derivatives.- 9 Two functions whose derivatives share values.- 10 Meromorphic functions sharing sets.

Meromorphic Functions over Non-Archimedean Fields

Preface. 1. Basic facts in rho-adic analysis. 2. Nevanlinna theory. 3. Uniqueness of meromorphic functions. 4. Differential equations. 5. Dynamics. 6. Holomorphic curves. 7. Diophantine Approximations. A. The Cartan conjecture for moving targets. Symbols. Index.

Dynamics of Transcendental Functions

Let f be a nonconstant meromorphic function. The sequence of the iterates of f is denoted by

On the unique range set of meromorphic functions

{f^0}=id,{f^1}=f,\cdots,{f^{n + 1}} = {f^n}(f), \cdots

On entire solutions of a certain type of nonlinear differential equation

Preface. 1: Nevanlinna theory. 1.1. Parabolic manifolds and Hermitian geometry. 1.2. The first main theorem. 1.3. Growths of meromorphic functions. 1.4. The lemma of logarithmic derivative. 1.5. Growth estimates of Wronskians. 1.6. The second main theorem. 1.7. Degenerate holomorphic curves. 1.8. Value distribution of differential polynomials. 1.9. The second main theorem for small functions. 1.10. Tumura-Clunie theory. 1.11. Generalizations of Nevanlinna theorem. 1.12. Generalizations of Borel theorem. 2: Uniqueness of meromorphic functions on C. 2.1. Functions that share four values. 2.2. Functions that share three values CM. 2.3. Functions that share pairs of values. 2.4. Functions that share four small functions. 2.5. Functions that share five small functions. 2.6. Uniqueness related to differential polynomials. 2.7. Polynomials that share a set. 2.8. Meromorphic functions that share the same sets. 2.9. Unique range sets. 2.10. Uniqueness polynomials. 3: Uniqueness of meromorphic functions on Cm. 3.1. Technical lemmas. 3.2. Multiple values of meromorphic functions. 3.3. Uniqueness of differential polynomials. 3.4. The four-value theorem. 3.5. The three-value theorem. 3.6. Generalizations of Rubel-Yangs theorem. 3.7. Meromorphic functions sharing one value. 3.8. Unique range sets of meromorphic functions. 3.9. Unique range sets ignoring multiplicities. 3.10. Meromorphic functions of order 4.8. Propagation theorems. 4.9. Uniqueness dealing with multiple values. 5: Algebroid functions of several variables. 5.1. Preliminaries. 5.2. Techniques of value distribution. 5.3. The second main theorem. 5.4. Algebroid reduction of meromorphic mappings. 5.5. The growth of branching divisors. 5.6. Reduction of Nevanlinna theory. 5.7. Generalizations of Malmquist theorem. 5.8. Uniqueness problems. 5.9. Multiple values of algebroid functions. References. Symbols. Index.

A new functional equation in the plasma inverse problem and its analytic properties

This paper studies the unique range set of meromorphic functions and shows that there exists a finite set S such that for any two nonconstant meromorphic functions f and g the condition Ef (S) = Eg(S) implies f _ g. As a special case this also answers an open question posed by Gross (1977) about entire functions and improves some results obtained recently by Yi.

Malmquist type theorem and factorization of meromorphic solutions of partial differential equations

Let f(z) denote an entire solution of a linear differential equation with entire coefficients. In this paper we have investigated λ 2 (f) and σ2 (f), the hyper-exponent of convergence of the zeros and the hyper-order of (f)respectively.