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. © 2009 Elsevier Inc. All rights reserved.
Cardinal, J. P. (2010). Symmetric matrices related to the Mertens function. Linear Algebra and Its Applications, 432(1), 161–172. https://doi.org/10.1016/j.laa.2009.07.035