Symmetric matrices related to the Mertens function
| dc.creator | Cardinal, Jean-Paul | |
| dc.date | 2008-11-22 | |
| dc.date | 2009-03-09 | |
| dc.date.accessioned | 2026-07-07T12:49:46Z | |
| dc.date.available | 2026-07-07T12:49:46Z | |
| dc.description | 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. | |
| dc.description | Version submitted to LAA; some new references | |
| dc.identifier | https://arxiv.org/abs/0811.3701 | |
| dc.identifier | http://arxiv.org/abs/0811.3701 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/222485 | |
| dc.subject | Number Theory | |
| dc.subject | 11C20; 11N56; 15A36; 15A60 | |
| dc.title | Symmetric matrices related to the Mertens function | |
| dc.type | text |