English

Une suite de matrices sym\'etriques en rapport avec la fonction de Mertens

Number Theory 2016-03-01 v4

Abstract

In this paper we explore a class of equivalence relations over N\N^\ast 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.

Keywords

Cite

@article{arxiv.0807.4145,
  title  = {Une suite de matrices sym\'etriques en rapport avec la fonction de Mertens},
  author = {Jean-Paul Cardinal},
  journal= {arXiv preprint arXiv:0807.4145},
  year   = {2016}
}

Comments

in French. D\'efinition 3.1 is slightly corrected. Nothing else changes since the correct definition was implicitly used in the previous versions of this article, specially in Lemme 3.5 and Section 4

R2 v1 2026-06-21T11:04:27.140Z