论文标题
质数定理中错误项的一些明确估计值
Some explicit estimates for the error term in the prime number theorem
论文作者
论文摘要
通过结合和改进最新技术和结果，我们提供了错误项的明确估计$ |π（x） - \ text {li}（x）| $，$ |θ（x）-x | $ and $ | ch（x）-x | $出现在质数定理中。例如，我们向所有$ x \ geq 2 $显示$ |ψ（x）-x | \ leq 9.39x（\ log x）^{1.515} \ exp（-0.8274 \ sqrt {\ log x}）$。我们的估计在很大程度上取决于Riemann Zeta功能的明确无零区域和零密度估计，并改善了$ x $的大值的质量计数功能的现有界限。
By combining and improving recent techniques and results, we provide explicit estimates for the error terms $|π(x)-\text{li}(x)|$, $|θ(x)-x|$ and $|ψ(x)-x|$ appearing in the prime number theorem. For example, we show for all $x\geq 2$ that $|ψ(x)-x|\leq 9.39x(\log x)^{1.515}\exp(-0.8274\sqrt{\log x})$. Our estimates rely heavily on explicit zero-free regions and zero-density estimates for the Riemann zeta-function, and improve on existing bounds for prime-counting functions for large values of $x$.
