A Remark on Meromorphic Functions Sharing Four Values

Reminiscence Of An Open Problem: Remarks On Nevanlinna's Four-Value-Theorem

“…Theorem (Chen, Chen, Ou & Tsai [3]). Suppose f and g share four values a ν , and assume also that there are integers 1 ≤ p < q such that each a ν -point is either a (p, q)-fold point for (f, g) or for (g, f ).…”

“…(A) is true since N (r, a ν ) = N s (r, a ν ) + S(r) for some ν and (R a ) for the same ν imply 3 2 N s (r, a κ ) ≤ N (r, a κ ) + S(r) (κ = ν), with 3 2 replaced by 2 if (a 1 , a 2 , a 3 , a 4 ) = −1. To prove (B) we may assume that a 4 is shared by counting multiplicities, thus…”