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

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

2009-06-11

arxiv.org/abs/0906.2132v1

Mathematics

Number Theory

12 pages, 6 tables

Scientific paper

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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