-
On uniqueness of meromorphic functions sharing finite sets
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 122, Number 6, December 2000
- pp. 1175-1203
- 10.1353/ajm.2000.0045
- Article
- Additional Information
- Purchase/rental options available:
We first study conditions for a polynomial P(w) to satisfy the condition that P(f) = cP(g) implies f = g for any nonzero constant c and nonconstant meromorphic functions f and g on c. Next, we give some sufficient conditions for a finite set S to be a uniqueness range set, namely, to satisfy the condition that f-1(S) = g-1(S) implies f = g for any nonconstant meromorphic functions f and g on c. For a set S, we consider a polynomial P(w) of degree q := #S which vanishes on S. Let P'(w) have distinct k zeros d1,..., dk and assume that k ≥ 4. We show that, if q > 2k + 12, P(dℓ) ≠ P(dm) (1 ≤ ℓ < m ≤ k) and P(d1) +...+ P(dk) ≠ 0, then S is a uniqueness range set, and discuss some other related subjects.