On Robin's criterion for the Riemann Hypothesis
| dc.creator | Choie, Y. -J. | |
| dc.creator | Lichiardopol, N. | |
| dc.creator | Moree, P. | |
| dc.creator | Sole, P. | |
| dc.date | 2006-04-13 | |
| dc.date | 2006-09-07 | |
| dc.date.accessioned | 2026-07-07T08:57:34Z | |
| dc.date.available | 2026-07-07T08:57:34Z | |
| dc.description | Robin's criterion states that the Riemann Hypothesis (RH) is true if and only if Robin's inequality sum_{d|n}d<e^{gamma}n loglog n is satisfied for n>=5041, where gamma denotes the Euler(-Mascheroni) constant. We show by elementary methods that if n>=37 does not satisfy Robin's criterion it must be even and is neither squarefree nor squarefull. Using a bound of Rosser and Schoenfeld we show, moreover, that n must be divisible by a fifth power >1. As a consequence we infer that RH holds true if and only if every natural number divisible by a fifth power >1 satisfies Robin's inequality. | |
| dc.description | 15 pages. Corrected version. In the first version in Theorem 5 (main result) it was falsely asserted that n must be superabundant, invalidating the proof. An alternative proof is provided in this version, some typos have been corrected, and the presentation has been improved | |
| dc.identifier | https://arxiv.org/abs/math/0604314 | |
| dc.identifier | http://arxiv.org/abs/math/0604314 | |
| dc.identifier | J. Theor. Nombres Bordeaux 19 (2007), 351-366. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/147018 | |
| dc.subject | Number Theory | |
| dc.subject | 11Y35; 11A25; 11A41 | |
| dc.title | On Robin's criterion for the Riemann Hypothesis | |
| dc.type | text |