发表机构
University of Lethbridge（莱斯布里奇大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为短区间内ζ函数的零点分布提供显式界，证明在临界带边缘附近，正比例的零点不靠近边缘，并给出具体数值比例。
AI 中文摘要
我们给出了在临界带边缘附近的短区间内，ζ函数的零点数量的显式界。最终我们证明，即使在短区间内，也有正比例的零点不会靠近临界带的边缘。例如，当h>100且t>10^100时，ζ的虚部在[t-h,t+h]内且实部在[1/16,15/16]内的零点比例至少为13%，而在t>10^43时已经可以获得正比例。
英文摘要
We provide explicit bounds on the number of zeros for $ζ$ in short intervals near the edge of the critical strip. Ultimately we show that even in short intervals a positive proportion of zeros will not be near the edge of the critical strip. For example with $h>100$ and $t>10^{100}$ the proportion of zeros of $ζ$ with imaginary part in $[t-h,t+h]$ which have real part in $[\frac{1}{16},\frac{15}{16}]$ is at least $13\%$ and a positive proportion is already obtained at $t>10^{43}$.
