Lines of research

Computation of the Mertens constants in arithmetic progressions (Prof. Alessandro Languasco)

  • In a recent paper, an elementary formula for the Mertens constants in arithmetic progressions appeared. These constants are connected with the asympotic behaviour of the Mertens product in arithmetic progressions. Such an elementary formula makes it possible to compute the constants using suitable values of Dirichlet L-series.
     

Computation of the Mertens and Meissel-Mertens constants for sums over arithmetic progressions (Prof. Alessandro Languasco)

  • In a recent paper (arxiv.org/abs/0906.2132), we described how to connect three Mertens constants in arithmetic progressions. These constants are involved in the asympotic behaviour of the Mertens product in arithmetic progressions (C(q,a)), in the sum of 1/p over primes in arithmetic progressions (M(q,a)) and in the sum of log(1-1/p)+1/p over primes in arithmetic progressions (B(q,a) which is also called the Meissel-Mertens constant). It turned out that, for every integer q>=3 and (q,a)=1, M(q,a) is the easiest computable constant and such a computation, together with the one we did for C(q,a), leads immediately to get B(q,a).