摘要
设f(z)=z+a_2z^2+a_3z^3+…∈S。Zalcman猜想|a_n^2-a_(2n-1)|≤(n-1)~2当n≥2时对函数类S成立,本文证明了当n=3时,Zalcman猜想是成立的。
Let f(z)=z+a_2z^2+a_3z^3+…∈S. Zalcman conjectured that |a_n^2-a_(2n-1)|≤(n-1)~2 (n=2, 3,…), which implied the famous Bieberbach conjecture. In this paper We establlshed the precise inequality |λa_3^(-2)-a_5^-|≤9λ-5 (λ≥1) The equality occurs if and only if f is a rotation of the Koebe function.
