2-Selmer Groups and the Birch-Swinnerton-Dyer Conjecture for the Congruent Number Curve
| dc.creator | Rhoades, Robert C. | |
| dc.date | 2007-06-29 | |
| dc.date.accessioned | 2026-07-07T08:13:06Z | |
| dc.date.available | 2026-07-07T08:13:06Z | |
| dc.description | We take an approach toward counting the number of n for which the curves E_n: y^2=x^3-n^2x have 2-Selmer groups of a given size. This question was also discussed in a pair of Invent. Math. papers by Roger Heath-Brown. We discuss the connection between computing the size of these Selmer groups and verifying cases of the Birch and Swinnerton-Dyer Conjecture. The key ingredient for the asymptotic formulae is the ``independence'' of the Legendre symbol evaluated at the prime divisors of an integer with exactly k prime factors. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/0706.4344 | |
| dc.identifier | http://arxiv.org/abs/0706.4344 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/132680 | |
| dc.subject | Number Theory | |
| dc.title | 2-Selmer Groups and the Birch-Swinnerton-Dyer Conjecture for the Congruent Number Curve | |
| dc.type | text |