On Plessner points of meromorphic functions

Slow Escaping Points of Meromorphic Functions

We show that for any transcendental meromorphic function f there is a point z in the Julia set of f such that the iterates fn(z) escape, that is, tend to ∞, arbitrarily slowly. The proof uses new covering results for analytic functions. We also introduce several slow escaping sets, in each of which fn(z) tends to ∞ at a bounded rate, and establish the connections between these sets and the Juli...

Fixed-points and uniqueness of meromorphic functions

Let () () z g z f , be two nonconstant meromorphic functions, and let k n, be two positive integers with. 7 3 + ≥ k n If () () k n f and () () k n g share () z f z CM; and () z g share , IM ∞ then (1) () () z tg z f = for ; 2 ≥ k (2) either () () 2 2 2 1 , cz cz e c z g e c z f − = = or () () z tg z f = for , 1 = k where , , 2 1 c c and c are three nonzero constants satisfying () 1 4 2 2 1 2 − ...

On Meromorphic Harmonic Functions with Respect to k-Symmetric Points

Fixed Points of Difference Operator of Meromorphic Functions

Let f be a transcendental meromorphic function of order less than one. The authors prove that the exact difference Δf =(z+1)-f(z) has infinitely many fixed points, if a ∈ ℂ and ∞ are Borel exceptional values (or Nevanlinna deficiency values) of f. These results extend the related results obtained by Chen and Shon.

Counting Meromorphic Functions with Critical Points of Large Multiplicities

We study the number of meromorphic functions on a Riemann surface with given critical values and prescribed multiplicities of critical points and values. When the Riemann surface is CP1 and the function is a polynomial, we give an elementary way of finding this number. In the general case, we show that, as the multiplicities of critical points tend to infinity, the asymptotic for the number of ...