UNICITY THEOREMS FOR MEROMORPHIC OR ENTIRE-FUNCTIONS

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