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- W4281253294 abstract "We give asymptotics for the number of isomorphism classes of elliptic curves over arbitrary number fields with certain prescribed local conditions. In particular, we count the number of points of bounded height on many genus zero modular curves, including the cases of $mathcal{X}(N)$ for $Nin{1,2,3,4,5}$, $mathcal{X}_1(N)$ for $Nin{1,2,dots,10,12}$, and $mathcal{X}_0(N)$ for $Nin{1,2,4,6,8,9,12,16,18}$. In all cases we give an asymptotic with an expression for the leading coefficient, and in many cases we also give a power savings error term. Our results for counting points on modular curves follow from more general results for counting points of bounded height on weighted projective spaces." @default.
- W4281253294 created "2022-05-23" @default.
- W4281253294 creator A5088486617 @default.
- W4281253294 date "2022-01-25" @default.
- W4281253294 modified "2023-09-30" @default.
- W4281253294 title "Rational Points of Bounded Height on Some Genus Zero Modular Curves over Number Fields" @default.
- W4281253294 doi "https://doi.org/10.48550/arxiv.2201.10624" @default.
- W4281253294 hasPublicationYear "2022" @default.
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