Journal of the Ramanujan Mathematical Society
Volume 29, Issue 2, June 2014 pp. 221–242.
A positive proportion of elliptic curves over Q have rank one
Authors:
Manjul Bhargava and Christopher Skinner
Author institution:Department of Mathematics, Princeton University, Princeton, NJ 08544
Summary:
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.
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