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

Manjul Bhargava, J. E. Cremona, Tom Fisher

Type: Article

Publication Date: 2015-08-31

Citations: 17

DOI: https://doi.org/10.1142/s1793042116500664

Abstract

We show that the proportion of plane cubic curves over [Formula: see text] that have a [Formula: see text]-rational point is a rational function in [Formula: see text], where the rational function is independent of [Formula: see text], and we determine this rational function explicitly. As a consequence, we obtain the density of plane cubic curves over [Formula: see text] that have points everywhere locally; numerically, this density is shown to be [Formula: see text].

Locations

International Journal of Number Theory - View
Warwick Research Archive Portal (University of Warwick) - View - PDF

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