The Growth of the Zero Dirichlet Series in Right Half Plane

The Dirichlet series of zero order in the half plane is studied and two theorems on their growth are obtained in this paper.

The Lower Order and Type of Solutions of Second Order Differential Equation

The main purpose of this paper is to study the lower order and type of second order differential equation w"(z)-A(z)w=0,where A(z)is a polynomial.In the case of A(z)=a_dz^d,the authors prove that the lower order and the type of all non-trivial solutions w of w"(z)-A(z)w=0 are equal to(d+2)/2 and(2(|a_d|)^(1/2))/(d+2)respectively.In the case of A(z)=a_dz^d+a_(d-1)z^(d-1)+…a_1z+a_0,a_d>0,a_(d-1)>0,…,a_1≥0,a_0≥0,the authors prove that the lower order of all non-trivial solutions w of w"(z)-A(z)w=0 is(d+2)/2.

Uniqueness Theorem of Algebroidal Function in the Unit Disc

In this paper, discussed are the problems about uniqueness of algebroidal functions in the unit disc with share-values in a sector domain instead of the whole disk. Results are obtained extending some uniqueness theorems of meromorphic functions.