A positive proportion of elliptic curves over Q have rank one

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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.

Original languageEnglish (US)
Pages (from-to)221-242
Number of pages22
JournalJournal of the Ramanujan Mathematical Society
Volume29
Issue number2
StatePublished - Jan 1 2014

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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