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.
|Original language||English (US)|
|Number of pages||22|
|Journal||Journal of the Ramanujan Mathematical Society|
|State||Published - Jan 1 2014|
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