A positive proportion of elliptic curves over Q have rank one

作者:Bhargava Manjul*; Skinner Christopher
来源:Journal of the Ramanujan Mathematical Society, 2014, 29(2): 221-242.

摘要

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.

  • 出版日期2014-6