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|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.|
|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|
|Pages:||221 - 242|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||JOURNAL OF THE RAMANUJAN MATHEMATICAL SOCIETY|
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