论文标题
Riemann Zeta功能的明确无零区域
Explicit zero-free regions for the Riemann zeta-function
论文作者
论文摘要
我们证明，Riemann Zeta -function $ζ（σ+ IT）$在该区域中没有零零，$σ\ geq 1-1/（55.241（\ log | t | T |）^{2/3} {2/3}（\ log log \ log \ log | t | t | t |）此外，我们改善了经典无零区域的常数，表明Zeta功能在该区域中没有零，$σ\ geq 1-1/（5.558691 \ log log | t |）$ for $ | t | \ geq 2 $。我们还提供新的界限，可用于$ | t | $的中间值。结合在一起，我们的结果改善了关键带中最大的已知零区域，价格为$ 3 \ cdot10^{12} \ leq | t | \ leq \ leq \ exp（64.1）$和$ | t | \ geq \ exp（1000）$。
We prove that the Riemann zeta-function $ζ(σ+ it)$ has no zeros in the region $σ\geq 1 - 1/(55.241(\log|t|)^{2/3} (\log\log |t|)^{1/3})$ for $|t|\geq 3$. In addition, we improve the constant in the classical zero-free region, showing that the zeta-function has no zeros in the region $σ\geq 1 - 1/(5.558691\log|t|)$ for $|t|\geq 2$. We also provide new bounds that are useful for intermediate values of $|t|$. Combined, our results improve the largest known zero-free region within the critical strip for $3\cdot10^{12} \leq |t|\leq \exp(64.1)$ and $|t| \geq \exp(1000)$.
