涉及全纯函数分担值的正规定则

Normal Families and Shared Values of Holomorphic Functions

摘要: 设F 为区域D 内的一族全纯函数，a₁、a₂ 为2个不同的有穷复数，M 为正整数. 若对任意的f∈F, f(z)-a₁ 至多有M 个零点, 且f -a_i(i=1,2) 的零点重级至少为2，则F 在区域D 内正规.

Abstract: Let F be a family of holomorphic functions in domain D, let a₁, a₂ be 2 distinct finite complex numbers, and let M be a positive integer. Suppose that each f∈F, f(z)-a₁ has at most M zeros, and all zeros of f -a_i(i=1,2) have multiplicity at least 2, then F is normal in D.