From explicit estimates for the primes to explicit estimates for the Möbius function II

We improve on all the results of [13] by incorporating the finite range computations performed since then by several authors. Thus we have \begin{align*} \Bigg|\sum_{n\le X}μ(n)\Bigg| &\le \frac{0.006688,X}{\log X},&&$\text{for }$ X\ge 1,798,118, \\Bigg|\sum_{n\le X}\frac{μ(n)}{n}\Bigg| & \le \frac{0.010032}{\log X},&& $\text{for }$ X\ge 617,990. \end{align*} We also improve on the method described in [13] by a simple remark.