A positive proportion of elliptic curves over Q have rank one

Manjul Bhargava; Christopher Skinner

A positive proportion of elliptic curves over Q have rank one

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	221-242
Number of pages	22
Journal	Journal of the Ramanujan Mathematical Society
Volume	29
Issue number	2
State	Published - Jun 2014

All Science Journal Classification (ASJC) codes

General Mathematics

Cite this

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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.",

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A positive proportion of elliptic curves over Q have rank one

Abstract

All Science Journal Classification (ASJC) codes

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