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arXiv · 0906.2132

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

Alessandro Languasco·Alessandro Zaccagnini
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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 $q \in \{3$, ..., $100\}$ and $(q, a) = 1$.

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Alessandro Languasco, Alessandro Zaccagnini. 2009-06-11. Computing the Mertens and Meissel-Mertens constants for sums over arithmetic progressions. https://doi.org/10.1080/10586458.2010.10390624

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