Explicit estimates for the summatory function of $\varLambda (n)/n$ from the one of $\varLambda (n)$
Volume 159 / 2013
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.
