Goldfeld conjecture for non-hyperelliptic direction
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866918356730249216 |
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| author | Jeong, Keunyoung Park, Junyeong |
| author_facet | Jeong, Keunyoung Park, Junyeong |
| contents | Since the curve $y^2 = x^6+1$ has a large automorphism group, there exist twist families arising from non-hyperelliptic directions. In this paper, we give an explicit upper bound on the average analytic rank of such a family, assuming the generalized Riemann hypothesis for the $L$-functions. Also, we propose an analogue of the Goldfeld conjecture for the family following Katz--Sarnak philosophy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21985 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Goldfeld conjecture for non-hyperelliptic direction Jeong, Keunyoung Park, Junyeong Number Theory Since the curve $y^2 = x^6+1$ has a large automorphism group, there exist twist families arising from non-hyperelliptic directions. In this paper, we give an explicit upper bound on the average analytic rank of such a family, assuming the generalized Riemann hypothesis for the $L$-functions. Also, we propose an analogue of the Goldfeld conjecture for the family following Katz--Sarnak philosophy. |
| title | Goldfeld conjecture for non-hyperelliptic direction |
| topic | Number Theory |
| url | https://arxiv.org/abs/2602.21985 |