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|Abstract:||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 ,andwe 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 ≈ 97 . 3%.|
|Electronic Publication Date:||5-Oct-2015|
|Citation:||Bhargava, Manjul, Cremona, John, Fisher, Tom. (2016). The proportion of plane cubic curves over Q that everywhere locally have a point. INTERNATIONAL JOURNAL OF NUMBER THEORY, 12 (1077 - 1092. doi:10.1142/S1793042116500664|
|Pages:||1077 - 1092|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||INTERNATIONAL JOURNAL OF NUMBER THEORY|
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