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The proportion of plane cubic curves over Q that everywhere locally have a point

joint with Manjul Bhargava and John Cremona

We show that the proportion of plane cubic curves over Qp that have a Qp - rational point is a rational function in p, where the rational function is independent of p, and we determine this rational function explicitly. As a consequence, we obtain the density of plane cubic curves over Q that have points everywhere locally; numerically, this density is shown to be appoximately 97.3%.


The proportion of plane cubic curves over Q that everywhere locally have a point   (14 pages)     dvi   ps   ps.gz   pdf