Daochun Sun

QUASIMEROMORPHIC MAPPINGS OF SEVERAL COMPLEX VARIABLES

Abstract The definitions of quasimeromorphic mappings from Cn to Pn1, wheren P 1 ≃ C ∪ { ∞ } , P 1 n = P 1 × P 1 × … × P 1 ( n - times ) are introduced. From an inequality of the value distribution of quasimeromorphic functions of single variable, it follows that a normal criterion for the family of quasimeromorphic functions of several complex variables. Futhermore, a normal criterion for the family of quasimeromorphic mappings from Cn to Pn1 has been obtained.

On the sharing values of algebroid functions and their derivatives

Abstract In this paper, we define the shared value of an algebroid function and its derivative on its Riemann surface. By considering the relationship between the shared values and the branch points of algebroid functions and their derivatives, we obtain some uniqueness theorems of algebroid functions sharing values with their derivatives, which extend 3 IM shared values theorem of nonconstant meromorphic functions and their derivatives obtained by Mues-Steinmetz and Gundersen.

On algebraic solutions of the second-order complex differential equations with entire algebraic element coefficients

Abstract The main purpose of this paper is to study the problems on the existence of algebraic solutions for some second-order complex differential equations with entire algebraic function element coefficients. Several theorems on the existence of solutions are obtained, which perfect the solution theory of linear complex differential equations.

The Borel directions of algebroidal function and its coefficient functions

Abstract In this article, the relationship between the Borel direction of algebroidal function and its coefficient functions is studied for the first time. To begin with, several theorems of algebroidal functions in unit disk are proved. By these theorems, some interesting conclusions are obtained.

Existence of meromorphic solutions of some higher order linear differential equations

This article discusses the problems on the existence of meromorphic solutions of some higher order linear differential equations with meromorphic coefficients. Some nice results are obtained. And these results perfect the complex oscillation theory of meromorphic solutions of linear differential equations.

On global meromorphic solutions of second-order linear differential equations with meromorphic coefficients

The main purpose of this article is to study the existence theories of global meromorphic solutions for some second-order linear differential equations with meromorphic coefficients, which perfect the solution theory of such equations.

On a new singular direction of quasimeromorphic mappings

Abstract By applying Ahlfors theory of covering surface, we establish a fundamental inequality for quasimeromorphic mapping in an angular domain. As an application, we prove the existence of a new singular direction for quasimeromorphic mapping f , namely, aprecise S direction, for which the spherical characteristic function S(r, f) is used as a comparison function.

On the inverse image set of rational functions

Abstract This article studies the inverse image of rational functions. Several theorems are obtained on the Julia set expressed by the inverse image, and a mistake is pointed out in H.Brolin theorem incidentally.

ON THE GROWTH OF INFINITE ORDER DIRICHLET SERIES

Abstract In this paper, the property of infinite order Dirichlet series in the half-plane are investigated. The more exact growth of infinite order Dirichlet series is obtained without using logarithm argument to the type-function for the first time.

The integration of algebroidal functions

In this paper, we introduce the integration of algebroidal functions on Riemann surfaces for the first time. Some properties of integration are obtained. By giving the definition of residues and integral function element, we obtain the condition that the integral is independent of path. At last, we prove that the integral of an irreducible algebroidal function is also an irreducible algebroidal function if all the residues at critical points are zeros.