Borel Direction Relative to Function-Values of Meromorphic Functions with Finite Logarithmic Order

程天佑(Peter Tien-Yu Chern)

《Tamkang Journal of Mathematics》 38卷3期 (2007/09) Pp. 217-224

並列摘要

It is shown that if f(z) is meromorphic in the complex plane C with finite positive logarithmic order λ and its characteristic function T(r, f) satisfies the growth condition (The equation is abbreviated), then there is a number θ with 0≤θ＜2π such that for each positive number ε, the expression (The equation is abbreviated) holds for any three distinct meromorphic functions a(subscript i)(z)(i=1, 2, 3) with T(r, a(subscript i))=o(U(r, f)/(log r)^2), as r→+∞, where n(r, φ, ε, f=a(z)) denotes the number of roots counting multiplicities of the equation f(z)=a(z) for z in the angular domain Ω (r, φ, ε)={z:|arg z-φ|＜ε,|z|＜r} where 0≤φ＜2π, ε＞0, U(r, f)=(log r)(superscript λ(r)), and limsup λ(r)=λ.