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

Volume 159 / 2013

Olivier Ramaré Acta Arithmetica 159 (2013), 113-122 MSC: Primary 11N05, 11M36; Secondary 11N37. DOI: 10.4064/aa159-2-2

Abstract

We prove that the error term $\sum _{\substack {n\le x}}\varLambda (n)/n-\log x+\gamma $ differs from $(\psi (x)-x)/x$ by a well controlled function. We deduce very precise numerical results from the formula obtained.

Authors

  • Olivier RamaréCNRS / Laboratoire Paul Painlevé
    Université Lille 1
    59 655 Villeneuve d'Ascq, France
    e-mail

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