A positive proportion of elliptic curves over Q have rank one
Author(s): Bhargava, Manjul; Skinner, Christopher M.
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http://arks.princeton.edu/ark:/88435/pr1d93h| Abstract: | We prove that, when all elliptic curves over Q are ordered by naive height, a positive proportion have both algebraic and analytic rank one. It follows that the average rank and the average analytic rank of elliptic curves are both strictly positive. |
| Publication Date: | Jun-2014 |
| Citation: | Bhargava, Manjul, Skinner, Christopher. (2014). A positive proportion of elliptic curves over Q have rank one. JOURNAL OF THE RAMANUJAN MATHEMATICAL SOCIETY, 29 (221 - 242 |
| ISSN: | 0970-1249 |
| EISSN: | 2320-3110 |
| Pages: | 221 - 242 |
| Type of Material: | Journal Article |
| Journal/Proceeding Title: | JOURNAL OF THE RAMANUJAN MATHEMATICAL SOCIETY |
| Version: | Author's manuscript |
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