关于单级零点较少的亚纯函数的一个改进的不等式

An Improved Inequality for Meromorphic Functions with Few Simple Zeros

设f(z)为复平面上非常数亚纯函数,满足N1)(r,1f)=S(r,f),而d为一非零常数.则T(r,f)<11N(r,f)+11N(r,1f′+df-1)+S(r,f),除非f(z)具有下列形式之一:(i)Ae-dz;(ii)1d(Ae-dz+1)2;(iii)1d(Ae-d2z-1)2;或(iv)Aedz(e-dz+12dA)2,其中A为一非零常数.

Suppose that f（z） is a non-constant meromorphic function in the complex plane satisfying Nl）（ r,1/f）=S（r,f） and d is non-zero constant. Then the author proves that T（r,f）〈11-N（r,f） ＋ 11-N（f,1/f＇＋df-1）＋S（r,f） except that f（z） is one of the following forms：（i）Ae^-dx;（ii）1/d（Ae^-dx＋1）^2 （iii） 1/d（Ae^-d/2x-1）^2;（iv） Ae^dx（e^-dx ＋ 1/2dA）^2, where A is a non-zero constant.