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

Olivier Ramaré (1, 2, 3)

1 I2M - Institut de Mathématiques de Marseille
2 CNRS - Centre National de la Recherche Scientifique
3 AMU - Aix Marseille Université

We prove two explicit estimates respectively slightly stronger than $|\sum_{d\le D}\mu(d)|/D \le 0.013/ \log D$ for every $D \ge 1 100 000$ and than $| \sum_{d\le D} \mu(d)/d| \le 0.026/ \log D$ for every $D \ge 61 000$.

Domaines: Théorie des nombres [math.NT]

Olivier Ramaré. From explicit estimates for primes to explicit estimates for the Möbius function. Acta Arithmetica, 2013, 157 (4), pp.365-379. ⟨10.4064/aa157-4-4⟩. ⟨hal-02572812⟩