The average analytic rank of elliptic curves
| dc.creator | Heath-Brown, D. R. | |
| dc.date | 2003-05-07 | |
| dc.date.accessioned | 2026-07-07T04:57:51Z | |
| dc.date.available | 2026-07-07T04:57:51Z | |
| dc.description | All the results in this paper are conditional on the Riemann Hypothesis for the L-functions of elliptic curves. Under this assumption, we show that the average analytic rank of all elliptic curves over Q is at most 2, thereby improving a result of Brumer. We also show that the average within any family of quadratic twists is at most 3/2, improving a result of Goldfeld. A third result concerns the density of curves with analytic rank at least R, and shows that the proportion of such curves decreases faster than exponentially as R grows. The proofs depend on an analogue of Weil's ``explicit formula''. | |
| dc.description | 28 pages | |
| dc.identifier | https://arxiv.org/abs/math/0305114 | |
| dc.identifier | http://arxiv.org/abs/math/0305114 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67404 | |
| dc.subject | Number Theory | |
| dc.title | The average analytic rank of elliptic curves | |
| dc.type | text |