Conversions explicites des nombres premiers vers la fonction de Möbius

Abstract

We prove that $|{\sum }_{n\le x}\mu (n)|\le x/160383$ for all $x\ge 8.4\times 10^9$ thus improving the record for this type of estimates which was $|{\sum }_{n\le x}\mu (n)|\le x/4345$ for all $x\ge 2160535$ and was due to Cohen, Dress and El Marraki. We also prove that $|{\sum }_{n\le x}\mu (n)|\le x/180194$ for all $x\ge 10^{19}$.

11 pages, In French