Let K be a compact subset of a connected Stein manifold X. We study algebraic properties of the ring of meromorphic functions on X without poles in K.

In this paper, Hinkkanen’s problem (1984) is completely solved, i.e., it is shown that any meromorphic function f is determined by its zeros and poles and the zeros of f (j) for j = 1, 2, 3, 4. To appear in J. Canad. Math. / Canad. J. Math.

This is an expanded version of one of the Lectures in memory of Lars Ahlfors in Haifa in 1996. Some mistakes are corrected and references added. This article is an exposition for non-specialists of Ahlfors’ work in the theory of meromorphic functions. When the domain is not specified we mean meromorphic functions in the complex plane C. The theory of meromorphic functions probably begins with t...

Let f be a nonconstant meromorphic function in the complex plane C. We shall use the standard notations in Nevanlinna’s value distribution theory of meromorphic functions such as T r, f , N r, f , and m r, f see, e.g., 1, 2 . The notation S r, f is defined to be any quantity satisfying S r, f o T r, f as r → ∞ possibly outside a set of E of finite linear measure. Let F be a family of meromorphi...

is the Nevanlinna characteristic of f [13]. Meromorphic functions of finite order have been extensively studied and they have numerous applications in pure and applied mathematics, e.g. in linear differential equations. In many applications a major role is played by the logarithmic derivative of meromorphic functions and we need to obtain sharp estimates for the logarithmic derivative as we app...

Analogies between the Nevanlinna theory and the theory of heights in number theory have motivated to the determination the precise error term of the second fundamental theorem of the Nevanlinna theory. The Nevanlinna secondary deeciency, introduced by P.M. Wong, gives the error term in a certain sense. We rst prove that, from a topological point of view, almost all meromorphic functions have se...

We introduce a notion of resultant of two meromorphic functions on a compact Riemann surface and demonstrate its usefulness in several respects. For example, we exhibit several integral formulas for the resultant, relate it to potential theory and give explicit formulas for the algebraic dependence between two meromorphic functions on a compact Riemann surface. As a particular application, the ...

the purpose of this paper is to derive various useful subordination properties and characteristics for certain subclass of multivalent meromorphic functions, which are defined here by the multiplier transformation. also, we obtained inclusion relationship for this subclass.