2008/07/25 by Jean-Paul Cardinal, Cardinal, Jean-Paul
Mathematics · #11C20 #11N56 #Advanced Algebra and Geometry #Analytic Number Theory Research #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.0807.4145
openalex publication_date 2008/07/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this paper we explore a class of equivalence relations over \N^∗ from which is constructed a sequence of symetric matrices related to the Mertens function. From numerical experimentations we suggest a conjecture, about the growth of the quadratic norm of these matrices, which implies the Riemann hypothesis. This suggests that matrix analysis methods may play a more important part in this classical and difficult problem.