Explicit estimates for the summatory function of $\Lambda (n)/ń$ from the one of $\Lambda (n)$

Olivier Ramaré (1, 2)

1 CNRS - Centre National de la Recherche Scientifique
2 LPP - Laboratoire Paul Painlevé - UMR 8524

We prove that the error term $\sum_{n\le x} \Lambda(n)/n − \log x + \gamma$ differs from $(\psi(x) − x)/x$ by a well controlled function. We deduce very precise numerical results from this formula.

Domaines: Théorie des nombres [math.NT]

Olivier Ramaré. Explicit estimates for the summatory function of $\Lambda (n)/ń$ from the one of $\Lambda (n)$. Acta Arithmetica, 2013, 159 (2), pp.113-122. ⟨10.4064/aa159-2-2⟩. ⟨hal-02572852⟩