From explicit estimates for the primes to explicit estimates for the Möbius function II
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912758671343616 |
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| author | Ramaré, Olivier Alterman, Sebastian Zuniga |
| author_facet | Ramaré, Olivier Alterman, Sebastian Zuniga |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_05969 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | From explicit estimates for the primes to explicit estimates for the Möbius function II Ramaré, Olivier Alterman, Sebastian Zuniga Number Theory 11A25, 11A41, 11N37 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. |
| title | From explicit estimates for the primes to explicit estimates for the Möbius function II |
| topic | Number Theory 11A25, 11A41, 11N37 |
| url | https://arxiv.org/abs/2408.05969 |