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...

We prove a unicity theorem of Nevanlinna for meromorphic mappings of P into Pm. 1. INTR~DuOTI~N As an application of Nevanlinna’s second main theorem and Borel’s lemma, R. Nevanlinna proved that for any two meromorphic functions in the complex plane @ on which they share four distinct values, then, these two meromorphic functions are the same up to a Mijbius transformation. Since then, there ha...

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...

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 ...