关于 Riemann-Zeta 函数零点密度估计

ON THE ZERO-DENSITY ESTIMATES FOR THE ZETA-FUNCTION OF RIEMANN

N(σ,T)表 Riemann-Zeta 函数ζ(s)在矩形,σ≤Re s≤1,|Ims|≤T,内的零点的个数,本文运用 Hala′asz 方法及大值方法,在一定的实区间内改进了 N(σ,T)的上界估值。

Let N(σ,T)denote the number of zeros of Riemann Zetafunction ξ(s)inthe intervalσ≤R_e(s)≤1, |I_m(s)|≤TThis paper shows that as σ near unity(?)This improves upon Ivié theorem as 9/10≤σ≤17/18