【摘要】 <正> §1 引言 由Picard定理知,开平面内的超越亚纯函数f(z)能取任何值无穷多次,至多除去两个例外值,即至多有两个Picard例外值存在,本文将要讨论的是一类函数的Picard例外值,对此问题,W.K.Hayman证明了以下结果:更多还原

【Abstract】 Let P(z) ,Q(z) be two non-constant polynomials and let t = degP(s), n=deg Q2(z), s be the number of distinct zeros of Q(z). In this paper, we discussed the Picard values of functions p(z) = P(f’(z)) -Q(f(z))and ψ(z) = P(f’(z))Q(f(z)) for f(z) transcendental entire or meromorphic. The following vesults are proved.1 )If s + 2t≤n(s + 3t + 1≤n), then for any transcendental entire(meromorphic) function f(z) , p(z) = f(f’(z)) -Q(f(z)) has at most ∞ as its picard value.2 ) If s + t n(s+ t + 1≤n), then for any transcendental entire (meromorphic) function f(z), ψ(z) = P(f’(z))Q(f(z)) has at most 0 and ∞ as its picard values.更多还原