We study the Mertens conjecture and revisit and improve the original constructivedisproof of Janos Pintz. We obtain a new lower bound for the minimal counterexample and new numerical results for this conjecture.
Mertens conjecture
Mathematics of Computing (acm G)
unknown (msc 11M06)
Other (theme 6)
Mathematics of Computation

Saouter, Y, & te Riele, H.J.J. (2014). Improved results on the Mertens conjecture. Mathematics of Computation, 83, 421–433. doi:10.1090/S0025-5718-2013-02716-0