摘要
Let f(z)=a_o+a_1z+… be holomorphic in the unit disk {z: |z|<1} and omit the values 0 and 1. It is proved in this paper that |a_1|≤2|a_0|{|log|a_0||+Γ~4(1/4)/4π~2-mRe(a_n^8 + 1)} where m>0.04 is a constant, ε=1 as |a_0|≤1 and ε=-1 as |a_0|>1. This result is a precise version of the well-known theorem of Landau and an improvement of the results of W. Lai~[1], J. A. Hempel~[2] and J. A. Jenkins~[3]
Let f（z）=a<sub>o</sub>+a<sub>1</sub>z+… be holomorphic in the unit disk {z: |z|<1} and omit the values 0 and 1. It is proved in this paper that |a<sub>1</sub>|≤2|a<sub>0</sub>|{|log|a<sub>0</sub>||+Γ<sup>4</sup>（1/4）/4π<sup>2</sup>-mRe（a<sub>n</sub><sup>8</sup> + 1）} where m>0.04 is a constant, ε=1 as |a<sub>0</sub>|≤1 and ε=-1 as |a<sub>0</sub>|>1. This result is a precise version of the well-known theorem of Landau and an improvement of the results of W. Lai<sup>[</sup>1], J. A. Hempel<sup>[</sup>2] and J. A. Jenkins<sup>[</sup>3]
基金
Project supported by the National Natural Science Foundation of China
