The distribution of the summatory function of the Möbius function
| dc.creator | Ng, Nathan | |
| dc.date | 2003-10-23 | |
| dc.date.accessioned | 2026-07-07T05:02:13Z | |
| dc.date.available | 2026-07-07T05:02:13Z | |
| dc.description | Let the summatory function of the Möbius function be denoted $M(x)$. We deduce in this article conditional results concerning $M(x)$ assuming the Riemann Hypothesis and a conjecture of Gonek and Hejhal on the negative moments of the Riemann zeta function. The main results shown are that the weak Mertens conjecture and the existence of a limiting distribution of $e^{-y/2}M(e^{y})$ are consequences of the aforementioned conjectures. By probabilistic techniques, we present an argument that suggests $M(x)$ grows as large positive and large negative as a constant times $\pm \sqrt{x} (\log \log \log x)^{5/4}$ infinitely often, thus providing evidence for an unpublished conjecture of Gonek's. | |
| dc.identifier | https://arxiv.org/abs/math/0310381 | |
| dc.identifier | http://arxiv.org/abs/math/0310381 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68970 | |
| dc.subject | Number Theory | |
| dc.subject | 11M26, 11N56 | |
| dc.title | The distribution of the summatory function of the Möbius function | |
| dc.type | text |