论文标题
张的ETA功能的X射线
X-Ray of Zhang's eta function
论文作者
论文摘要
对水平曲线的研究$η（s）= 0 $和$η（s）= 0 $的真实部分，对于$η（s）=π^{ - s/2}γ（s/2）ζ^\ prime（s）$，提供了$ $ q（S）$和$ζ^\ prime（S）的零的新分类。数值证据表明，间隙的统计数据（$ζ$的零之间）或距关键线的距离（对于$ζ^\ prime $的零）与分类有关。定理6给出了我们归类为2型的零的Soundararajan的全部猜想。我们假设整个过程中假设Riemann假设。
Study of the level curves the real part of $η(s)=0$ and imaginary part of $η(s)=0$, for $η(s)=π^{-s/2}Γ(s/2)ζ^\prime(s)$ gives a new classification of the zeros of $ζ(s)$ and of $ζ^\prime(s)$. Numerical evidence indicates that the statistics of the gaps (between zeros of $ζ$), or distance from the critical line (for zeros of $ζ^\prime$) is related to the classification. Theorem 6 gives the full conjecture of Soundararajan for the zeros we classify as type 2. We assume the Riemann Hypothesis throughout.
