Symmetric matrices related to the Mertens function
  In this paper we explore a family of congruences over $\N^\ast$ from which one builds a sequence of symmetric matrices related to the Mertens function.   From the results of numerical experiments, we formulate a conjecture about the growth of the quadratic norm of these matrices, which implies the Riemann hypothesis. This suggests that matrix analysis methods may come to play a more important role in this classical and difficult problem. 
Jean-Paul Cardinal