■函数零点密度的估计

An Estimation for -Function Zero Points Density

设 N(a,T)表示ζ(δ+it)在a≤δ≤1,|t|≤T 中的零点个数,我们证明了:当(509)≤a<1时有N(a,T)<<T(229(1-a))/(140(2a-1))+1.从而改进了潘承洞和潘承彪《哥德巴赫猜想》一书中关于ζ函数零点密度估计的著名结果。

Let N(a,T)denote the number ζ(δ+it)with α≤σ≤1 and |t|.T,The authors have proved the following : N(a.T)<<T(229(1-a))/(140(2a-1)). Here,The outcome makes an improvement on the well-known result reached by Pan Chengdong and Pen Chengbiao in connection with ζ-function zero points density.