关于Springer猜想的一个新结果

A New Result on the Springer's Conjecture

设∑′表示在区域1<|z|<∞中单叶亚纯函数 F(z)=z+sum from n=1 to ∞b_nz^(-n)所组成的函数族.若G是产F∈∑′的逆函数,而G在∞邻域的展式是 G(ω)=ω-sum from N=1 to ∞B_Nω^(-N)·G.Springer证明了:|B_3|≤1;

Suppose Springer conjectured thatIn this article using the Grunsky inequality and the formula of the Grunsky coefficients the author has proved that the Springer's conjecture is right when allterms b l1 b l 2…blp in the expression of B2N-1 are real numbers of the same sign or when all coefficients bn of F(z) are positive real numbers.