Tom Fisher's Home Page

joint with Manjul Bhargava and John Cremona

We show that the proportion of plane cubic curves over Q_p that have a Q_p - 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)          

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