Global discrepancy and small points on elliptic curves
| dc.creator | Baker, Matthew | |
| dc.creator | Petsche, Clayton | |
| dc.date | 2005-07-11 | |
| dc.date.accessioned | 2026-07-07T05:21:36Z | |
| dc.date.available | 2026-07-07T05:21:36Z | |
| dc.description | Let E be an elliptic curve defined over a number field k. In this paper, we define the ``global discrepancy'' of a finite set Z of algebraic points on E which in a precise sense measures how far the set is from being adelically equidistributed. We then prove an upper bound for the global discrepancy of Z in terms of the average canonical height of points in Z. We deduce from this inequality a number of consequences. For example, we give a new and simple proof of the Szpiro-Ullmo-Zhang equidistribution theorem for elliptic curves. We also prove a non-archimedean version of the Szpiro-Ullmo-Zhang theorem which takes place on the Berkovich analytic space associated to E. We then prove some quantitative `non-equidistribution' theorems for totally real or totally p-adic small points. The results for totally real points imply similar bounds for points defined over the maximal cyclotomic extension of a totally real field. | |
| dc.description | 33 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0507228 | |
| dc.identifier | http://arxiv.org/abs/math/0507228 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75751 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.title | Global discrepancy and small points on elliptic curves | |
| dc.type | text |