Zeta函数与它的导函数的零点分布

On Distribution of Zeros of Zeta- function and its Deivative Function

目的是推广美国著名数学家N．Levinson关于RiemannZeta函数和它的导函数的零点分布结果，笔者用对称分析法推出了三个新定理．

Let η(s ) =ξ(s) + λξ' (s )/logT, where ξ(s) be Riemann Zeta -- function, then number of the zeal of η(s) is free O(lopT) to one of ξ(s) on 1/2 < σ < 2, T≤ t ≤ T + U, uniformally for 0≤ λ≤2-log2(logT)/logT, where T be a large positive number and log2 T ≤U ≤T(logT)c(c > 0) .