It is shown that a real-valued formal meromorphic function on a formal generic submanifold of finite Kohn-Bloom-Graham type is necessarily constant.

Dealing with a question initiated by Liu [Meromorphic functions sharing set applications to difference equations, J. Math. Anal. Appl., 2009], we have investigated the situation when finite order entire function and its shift differential operator share two sets of small functions. Our result has improved extended results Chen-Chen [Entire their operators or shifts, Slovaca, 2013] Cui-Chen [The...

If the preimage of a four-point set under a meromorphic function belongs to the real line then the image of the real line is contained in a circle in the Riemann sphere. We include an application of this result to holomorphic dynamics: if the Julia set of a rational function is contained in a smooth curve then it is contained in a circle. If the full preimage of a two-point set under a rational...

In this paper, we study the relationship between a meromorphic function and its k-th order derivative which share a small function with weight(multiplicities) l(a positive integer)ignoring multiplicity. MR(2010) Subject Classification: 30D35.

In this paper, we investigate the relationship between a meromorphic function f(z) and its difference operator when they share two sets, and give some interesting results.

We prove that Mues’ conjecture holds for the secondand higher-order derivatives of a square and higher power of any transcendental meromorphic function. 2000 Mathematics Subject Classification. 30D35.

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

Hurwitz spaces are spaces of pairs S, f where S is a Riemann surface and f : S → ̂ C a meromorphic function. In this work, we study 1-dimensional Hurwitz spaces Hp of meromorphic p-fold functions with four branched points, three of them fixed; the corresponding monodromy representation over each branched point is a product of p − 1 /2 transpositions and the monodromy group is the dihedral group ...

is called Riemann’s Theorem and guarantees the existence of functions whose poles can only occur at certain places. In fact, if D = ∑ ni(Pi) − ∑ mj(Qj), then H(D) consists of all functions f with zeros of order ≥ mj at Qj and poles of order ≤ ni at Pi. Riemann’s original motivation was to construct meromorphic functions on compact Riemann surfaces. For example, the meromorphic functions on a to...

where F is a polynomial in the first k+ 1 variables, whose coefficients are analytic functions of the independent variable z. If the conditions of Cauchy's theorem for the existence and uniqueness of the solution are satisfied, then (0.1) determines an analytic function in a neighbourhood of a given point z0. One of the most difficult problems in the analytic theory of differential equations is...