Bibliographic Details
| Title: |
Sharp estimates for the M{o}bius function with coprimality restrictions. |
| Authors: |
de Camargo, André Pierro1 (AUTHOR) |
| Source: |
Mathematics of Computation. Sep2026, Vol. 95 Issue 361, p2515-2538. 24p. |
| Subjects: |
Möbius function, Arithmetic functions, Mathematical constants, Number theory, Addition (Mathematics) |
| Abstract: |
We prove that, for x > q (x real), uniformly in q \geq 2, \begin{equation*} \frac {\varphi (q)}{q}\bigg |\sum _{\substack {j \leq x \\ (j,q) = 1}} \frac {\mu (j)}{j}\bigg | \log (x/q) \leq 0.3055. \end{equation*} The constant 0.3055 is optimal up to the third decimal place. This answers a question of Ramaré [Math. Comp. 84 (2015), pp. 1359–1387]. Sharper results are obtained for larger integers q. Similar results are obtained for the sums \displaystyle \sum _{\substack {j \leq x \\ (j,q) = 1}} \mu (j). [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
