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

Abstract

We give explicit numerical values with 100 decimal digits for the Mertens constant involved in the asymptotic formula for $\sum _{\begin{array}{c}p\le xp\equiv a\mathrm{mod}q\end{array}}1/p$ and, as a by-product, for the Meissel-Mertens constant defined as ${\sum }_{p\equiv a\mathrm{mod}q}(\log (1-1/p)+1/p)$, for $q\in \{3$, ..., $100\}$ and $(q,a)=1$.

12 pages, 6 tables

References in corpus (1)

• On the constant in the Mertens product for arithmetic progressions. II. Numerical values

Cited by in corpus (3)

• Large bias for integers with prime factors in arithmetic progressions
• Euler constants from primes in arithmetic progression
• On the mean values of the error terms in Mertens' theorems