Title :

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

Author(s) :

Ramaré, Olivier [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Centre National de la Recherche Scientifique [CNRS]

Journal title :

ACTA ARITHMETICA

Pages :

113-122

Publisher :

Instytut Matematyczny PAN

Publication date :

2013

HAL domain(s) :

Mathématiques [math]/Théorie des nombres [math.NT]

English abstract : [en]

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.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.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Submission date :

2025-01-24T16:46:46Z