Abstract
In 1921, G. Pólya showed that non-constant meromorphic functions ϕ and ψ of finite genera on the complex plane C are necessarily equal if there are distinct five values ai(1 ≦ i ≦ 5) such that ϕ(z) — ai and ψ(z) — ai have the same zeros of the same multiplicities for each i ([8]). Afterwards, R. Nevanlinna obtained the same conclusion for arbitrary ϕp and ψ satisfying ϕ— 1(ai) = ψ— 1(1 ≦ i ≦ 5) regardless of multiplicities. And, some other results relating to this were given by H. Cartan ([2], [3]), E. M. Schmid ([9]) and others. The purpose of this paper is to give some types of generalizations of these results to the case of meromorphic maps into the N-dimensional complex projective space PN(C).
Publisher
Cambridge University Press (CUP)
Reference9 articles.
1. Sur les zeros des combinaisons lineaires de p fonctions holomorphes donnees;Cartan;Mathematica,1933
2. Sur les zéros des fonctions entières
3. Einige Eindeutigkeitssätze in der Theorie der Meromorphen Funktionen
4. Extensions of the big Picard's theorem
5. Sur les systemes de fonctions holomorphes a varietes lineaire lacunaires et leurs applications;Cartan;Ann. E. N. S.,1928
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