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Working from a half-plane result of Fletcher and Langley, we show that if f is an integer-valued function on some subset of the natural numbers of positive lower density and is meromorphic of sufficiently small exponential type in the plane, then f is a polynomial.

We prove that if two transcendental meromorphic functions share all limit values from a set of positive linear measure on a rectifiable Jordan arc, then they share all limit values.

We give a positive answer to a question of Horst Tietz. A theorem of his that is related to the Mittag-Leffler theorem looks like a duality restult under some locally convex topology on the space of meromorphic functions. Tietz has posed the problem of finding such a topology. It is shown that a topology introduced by Holdguün in 1973 solves the problem. The main tool in the study of this topology is a projective description of it that is derived here. We also argue that Holdgrün's topology is the natural locally convex topology on the space of meromorphic functions.

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Integer Points of Meromorphic Functions

Meromorphic functions with shared limit values of positive linear measure

The locally convex topology on the space of meromorphic functions

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3 results

Integer Points of Meromorphic Functions

Meromorphic functions with shared limit values of positive linear measure

The locally convex topology on the space of meromorphic functions