On the ring of locally bounded Nash meromorphic functions

Valuations on Meromorphic Functions of Bounded Type

The primary purpose of this paper is to show that every valuation on the field of meromorphic functions of bounded type on a finitely sheeted unlimited covering Riemann surface is a point valuation if and only if the same is true on its base Riemann surface. The result is then applied to concrete examples and some related results are obtained. Any valuation on the field M(W) of single valued me...

On Meromorphic Functions of Bounded Characteristic

Some Unsolved Problems on Meromorphic Functions of Uniformly Bounded Characteristic

The family UBC(R) of meromorphic functions of uniformly bounded characteristic in a Rieman surface R is defined in terms of the Shimizu-Ahlfors characteristic function. There are some natural parallels between UBC(R) and BMOA(R), the fsmily of holomorr.hc f11nctonz of bounded mesn oscilltion in R. After a survey some open problems are proposed in contrast with BMOA(R).

The ring of real-continuous functions on a topoframe

 A topoframe, denoted by $L_{ tau}$,  is a pair $(L, tau)$ consisting of a frame $L$ and a subframe $ tau $ all of whose elements are complementary elements in $L$. In this paper, we define and study the notions of a $tau $-real-continuous function on a frame $L$ and the set of real continuous functions $mathcal{R}L_tau $ as an $f$-ring. We show that $mathcal{R}L_{ tau}$ is actually a generali...

On the Genus of Meromorphic Functions

We define the class of Left Located Divisor (LLD) meromorphic functions and their vertical order m0(f) and their convergence exponent d(f). When m0(f) ≤ d(f) we prove that their Weierstrass genus is minimal. This explains the phenomena that many classical functions have minimal Weierstrass genus, for example Dirichlet series, the Γ-function, and trigonometric functions. 1. LLD meromorphic funct...