On the Jacobian of hyperelliptic curves y2 = x5 + m2

作     者：Jeong, Keunyoung Park, Junyeong Yhee, Donggeon 

作者机构：Department of Mathematical Sciences Ulsan National Institute of Science and Technology UNIST-gil 50 Ulsan44919 Korea Republic of  San 31 Hyoja-Dong Nam-Gu Gyeongsangbuk-do Pohang-si790-784 Korea Republic of Industrial and Mathematical Data Analytics Research Center Seoul National University Gwanak-Ro 1 Gwanak-Gu Seoul Korea Republic of 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2021年

核心收录：

主　　题：Geometry 

摘      要：MSC Codes 11G30, 11G10, *** 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. © 2021, CC BY-NC-ND.