We give explicit numerical values with 100 decimal digits for the Mertens constant involved in the asymptotic formula for $\sum\limits_{\substack{p\leq x\\ p\equiv a \bmod{q}}}1/p$ and, as a by-product, for the Meissel-Mertens constant defined as $\sum_{p\equiv a \bmod{q}} (\log(1-1/p)+1/p)$, for $q \in \{3$, \dots, $100\}$ and $(q,a) = 1$. The complete set of results can be downloaded from the webpage: \url{http://www.math.unipd.it/~languasc/Mertens-comput.html}
Computing the Mertens and Meissel-Mertens Constants for Sums over Arithmetic Progressions
LANGUASCO, ALESSANDRO;
2010
Abstract
We give explicit numerical values with 100 decimal digits for the Mertens constant involved in the asymptotic formula for $\sum\limits_{\substack{p\leq x\\ p\equiv a \bmod{q}}}1/p$ and, as a by-product, for the Meissel-Mertens constant defined as $\sum_{p\equiv a \bmod{q}} (\log(1-1/p)+1/p)$, for $q \in \{3$, \dots, $100\}$ and $(q,a) = 1$. The complete set of results can be downloaded from the webpage: \url{http://www.math.unipd.it/~languasc/Mertens-comput.html}
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