This paper considers the oscillation on meromorphic solutions of the second-order linear differential equations with the form f'' + A(z)f = 0, where A(z) is a meromorphic function with [p, q]-order. We obtain some theorems which are the improvement and generalization of the results given by Bank and Laine, Cao and Li, Kinnunen, and others.

We prove that if X is a meromorphic subvariety of a commutative meromorphic group G and X has finite stabilizer, then X is contained in a translate of an algebraic subgroup of G. We give an application with a “diophantine” flavour.

1. Harmonic analysis on H 2. Meromorphic continuation up to the critical line 3. Sobolev inequality/imbedding 4. Eventually-vanishing constant terms 5. Compactness of Sob(Γ\H)a → L(Γ\H) 6. Discreteness of cuspforms 7. Meromorphic continuation beyond the critical line 8. Discrete decomposition of truncated Eisenstein series 9. Appendix: Friedrichs extensions 10. Appendix: simplest Maass-Selberg ...

This paper uses the Tsuji’s characteristic to investigate the uniqueness of transcen- dental meromorphic function with shared values in an angular domain dealing with the multiple values which improve a result of J. Zheng.

the aim of this paper is to prove some inequalities for p-valent meromorphic functions in thepunctured unit disk δ* and find important corollaries.

In this article, a meromorphic function means meromorphic in the open complex plane. We assume that the reader is familiar with the Nevanlinna theory of meromorphic functions and the standard notations such as T r, f , m r, f , N r, f ,N r, f , and so on. Let f and g be two nonconstant meromorphic functions; a meromorphic function a z /≡∞ is called a small functions with respect to f provided t...

By using the second main theorem of the meromorphic function on annuli, we investigate the problem on two meromorphic functions partially sharing five or more values and obtain some theorems that improve and generalize the previous results given by Cao and Yi.

The main purpose of this paper is to study the exceptional values of meromorphic function and its derivative on annulus. We also give some theorems and corollaries about exceptional values of meromorphic function on the annulus, which are the improvement of the previous results given by Chen and Wu.

By using Tsuji's characteristic, we investigate uniqueness of meromorphic functions in an angular domain dealing with the shared set, which is different from the set of the paper (Lin et al., 2006) and obtain a series of results about the unique range set of meromorphic functions in angular domain.

The main purpose of this paper is to consider the oscillation theory on meromorphic solutions of second order linear differential equations of the form f ′′ + A(z)f = 0 where A is meromorphic in the complex plane. We improve and extend some oscillation results due to Bank and Laine, Kinnunen, Liang and Liu, and others.