2008/11/22 by Jean-Paul Cardinal, Cardinal, Jean-Paul
Physics and Astronomy · Computer Science · Mathematics · #Advanced Mathematical Theories and Applications #Matrix Theory and Algorithms #Mathematical Inequalities and Applications
paper · pdf · doi:10.48550/arxiv.0811.3701
In this paper we explore a family of congruences over \N^∗ 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.