Variations on a theme of Runge: effective determination of integral points on certain varieties
| dc.creator | Levin, Aaron | |
| dc.date | 2008-05-09 | |
| dc.date.accessioned | 2026-07-07T09:38:02Z | |
| dc.date.available | 2026-07-07T09:38:02Z | |
| dc.description | We consider some variations on the classical method of Runge for effectively determining integral points on certain curves. We first prove a version of Runge's theorem valid for higher-dimensional varieties, generalizing a uniform version of Runge's theorem due to Bombieri. We then take up the study of how Runge's method may be expanded by taking advantage of certain coverings. We prove both a result for arbitrary curves and a more explicit result for superelliptic curves. As an application of our method, we solve certain equations involving squares in products of terms in an arithmetic progression. | |
| dc.description | 30 pages | |
| dc.identifier | https://arxiv.org/abs/0805.1345 | |
| dc.identifier | http://arxiv.org/abs/0805.1345 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/160666 | |
| dc.subject | Number Theory | |
| dc.subject | 11D41, 11D72, 11G35 | |
| dc.title | Variations on a theme of Runge: effective determination of integral points on certain varieties | |
| dc.type | text |