The average analytic rank of elliptic curves with prescribed level structure
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908545996292096 |
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| author | Cho, Peter J. Jeong, Keunyoung Park, Junyeong |
| author_facet | Cho, Peter J. Jeong, Keunyoung Park, Junyeong |
| contents | Assuming the Hasse--Weil conjecture and the generalized Riemann hypothesis for the $L$-functions of the elliptic curve, we give an upper bound of the average analytic rank of elliptic curves over the number field with a level structure such that the corresponding compactified moduli stack is representable by the projective line. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_05817 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The average analytic rank of elliptic curves with prescribed level structure Cho, Peter J. Jeong, Keunyoung Park, Junyeong Number Theory 11G05, 11M26 (primary), 11F72, 14D23 (secondary) Assuming the Hasse--Weil conjecture and the generalized Riemann hypothesis for the $L$-functions of the elliptic curve, we give an upper bound of the average analytic rank of elliptic curves over the number field with a level structure such that the corresponding compactified moduli stack is representable by the projective line. |
| title | The average analytic rank of elliptic curves with prescribed level structure |
| topic | Number Theory 11G05, 11M26 (primary), 11F72, 14D23 (secondary) |
| url | https://arxiv.org/abs/2312.05817 |