关于亚纯函数唯一性问题的注记

NOTE ON THE UNIQUENESS OF MEROMORPHIC FUNCTIONS

本文应用 Nevanlinna 理论,研究了在相同点覆盖二个有限集合的整函数与具有两个亏值的亚纯函数的唯一性问题,改进了 F.Gross,C.C.Yang,熊庆来,扬乐,谢晖春和本文作者的有关定理.

In this paper we prove the following theorems: Theorem 1 Let S_1={a_1,a_2},S_2={b_1,b_2}be two pairs of distinct elements with a_1+a_2=b_1+b_2 but a_1a_2≠b_1b_2.Suppose that there are two nonconstant entire function f and g such that E_f(S_i)=E_(?)(S_i)for i=1,2.If N(r,1/f-a_1) <(λ+o(1))T(r,f)(r∈I),where λ<1/3,I(?)(0,+∞),and mes I=+∞,then either f≡g,or f+g≡a_1+a_2,or(f-a_1)(g-a_j)≡(-1)^(l+j)(a_1-a_2)~2(j=1,2). Theorem 2 Let a_1,a_2,a_3 be distinct finite complex numbers,and a_i≠0 (i=1,2,3).Suppose that f and g are two nonconstant meromorphic functions in the complex plane. If Θ(0,f)+Θ(∞,f)>λ+2/λ+1, Θ(0,g)+Θ(∞,g)>λ+2/λ+1, and (?)_λ)(a_i,f)=(?)_λ)(a_i,g)(i=1,2,3), where λ is a positive integer,then f≡g.