Computing the Mertens and Meissel-Mertens constants for sums over arithmetic progressions

Alessandro Languasco, Alessandro Zaccagnini

We give explicit numerical values with 100 decimal digits for the Mertens constant involved in the asymptotic formula for $\sum _{\begin{array}{c}p\le xp\equiv a\mathrm{mod}q\end{array}}1/p$ a…