Counting elliptic curves with a cyclic $m$-isogeny over $\mathbb{Q}$
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917566218240000 |
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| author | Molnar, Grant |
| author_facet | Molnar, Grant |
| contents | Using methods from analytic number theory, for $m > 5$ and for $m = 4$, we obtain asymptotics with power-saving error terms for counts of elliptic curves with a cyclic $m$-isogeny up to quadratic twist over the rational numbers. For $m > 5$, we then apply a Tauberian theorem to achieve asymptotics with power saving error for counts of elliptic curves with a cyclic $m$-isogeny up to isomorphism over the rational numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06815 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Counting elliptic curves with a cyclic $m$-isogeny over $\mathbb{Q}$ Molnar, Grant Number Theory Algebraic Geometry 11N45, 11G05, 11Y40 Using methods from analytic number theory, for $m > 5$ and for $m = 4$, we obtain asymptotics with power-saving error terms for counts of elliptic curves with a cyclic $m$-isogeny up to quadratic twist over the rational numbers. For $m > 5$, we then apply a Tauberian theorem to achieve asymptotics with power saving error for counts of elliptic curves with a cyclic $m$-isogeny up to isomorphism over the rational numbers. |
| title | Counting elliptic curves with a cyclic $m$-isogeny over $\mathbb{Q}$ |
| topic | Number Theory Algebraic Geometry 11N45, 11G05, 11Y40 |
| url | https://arxiv.org/abs/2401.06815 |