Characteristic Functions and Borel Exceptional Values ofE-Valued Meromorphic Functions

Characteristic Functions and Borel Exceptional Values of E-Valued Meromorphic Functions

and Applied Analysis 3 Let n r, f or n r, ∞̂ denote the number of poles of f z in |z| ≤ r and let n r, a, f denote the number of a-points of f z in |z| ≤ r, counting with multiplicities. Define the volume function associated with E-valued meromorphic function f z by V ( r, ∞̂, f V r, f 1 2π ∫ Cr log ∣∣ ∣ ∣ r ξ ∣∣ ∣ ∣Δ log ∥ ∥f ξ ∥ ∥dx ∧ dy, ξ x iy, V ( r, a, f ) 1 2π ∫ Cr log ∣ ∣ ∣ ∣ r ξ ∣ ∣ ∣ ∣Δ...

Five-value rich lines‎, ‎Borel directions and uniqueness of meromorphic functions

For a meromorphic function $f$ in the complex plane, we shall introduce the definition of five-value rich line of $f$, and study the uniqueness of meromorphic functions of finite order in an angular domain by involving the five-value rich line and Borel directions. Finally, the relationship between a five-value rich line and a Borel direction is discussed, that is, every Borel direction of $f$ ...

On Meromorphic Functions of Bounded Characteristic

Normal families of meromorphic functions sharing values or functions

* Correspondence: jiangyunbo@ss. buaa.edu.cn School of Mathematics and Systems Science and LMIB, Beihang University, Beijing, 100191, People’s Republic of China Abstract In this paper, we investigate the normal families of meromorphic functions concerning shared values and shared analytic functions and prove some normal criteria that generalize or extend some results obtained by Q. C. Zhang, Y....

Transcendental Meromorphic Functions with Three Singular Values

Every transcendental meromorphic function f in the plane which has only three critical values satisfies lim inf r→∞ T (r, f) log r ≥ √ 3