Unicity theorems for meromorphic or entire functions

Publisher: Cambridge University Press

E-ISSN: 1755-1633|49|2|257-265

ISSN: 0004-9727

Source: Bulletin of the Australian Mathematical Society, Vol.49, Iss.2, 1994-04, pp. : 257-265

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Abstract

In this paper, we prove that there exist three finite sets Sj (j = 1, 2, 3) such that any two non-constant meromorphic functions f and g satisfying Ef(Sj) = Eg(Sj) for j = 1,2,3 must be identical. As a particular case of the above result, we obtain that there exist two finite sets Sj (j = 1, 2) such that any two non-constant entire functions f and g satisfying Ej(Sj) = Eg(Sj) for j = 1, 2 must be identical, which answers a question posed by Gross.