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ON THE JACOBIAN OF A FAMILY OF HYPERELLIPTIC CURVES
- Author(s)
- Jeong, Keunyoung, Park, Junyeong, Yhee, Donggeon
- Issued Date
- 2023-01
- Citation
- OSAKA JOURNAL OF MATHEMATICS, v.60, no.1, pp.43 - 60
- Abstract
- In this paper, we study the algebraic rank and the analytic rank of the Jacobian of hyperelliptic curves y2 = x5 + m2 for integers m. Namely, we first provide a condition on m that gives a bound of the size of Selmer group and then we provide a condition on m that makes L-functions non-vanishing. As a consequence, we construct a Jacobian that satisfies the rank part of the Birch–Swinnerton-Dyer conjecture.
- Publisher
- Osaka Daigaku Shigakkai
- ISSN
- 0030-6126
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