ON THE JACOBIAN OF A FAMILY OF HYPERELLIPTIC CURVES

Jeong, Keunyoung; Park, Junyeong; Yhee, Donggeon

Osaka Journal of Mathematics, 2023, 60(1), 43-60

アクセス数:69件（2025-04-19 20:30 集計）

固定URL: https://doi.org/10.18910/89992

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タイトル	ON THE JACOBIAN OF A FAMILY OF HYPERELLIPTIC CURVES
著者	著者名 Jeong, Keunyoung
	著者名 Park, Junyeong
	著者名 Yhee, Donggeon
抄録	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.
出版者	Osaka University and Osaka Metropolitan University, Departments of Mathematics
収録物名	Osaka Journal of Mathematics
巻(号)	60(1)
ページ	43-60
刊行年月	2023-01
言語	英語
ハンドルURL	https://hdl.handle.net/11094/89992
DOI	https://doi.org/10.18910/89992
PISSN	00306126
NCID	AA00765910
アクセス権	open access
出版タイプ	Version of Record
カテゴリ	紀要論文 Departmental Bulletin Paper
カテゴリ	Osaka Journal of Mathematics / Volume 60, Number 1 （2023-1）

資源タイプ	紀要論文
ローカル資源タイプ	紀要論文
DCMI資源タイプ	text
DCTERMS.bibliographicCitation	Osaka Journal of Mathematics. 2023, 60(1), p. 43-60
DC.title	ON THE JACOBIAN OF A FAMILY OF HYPERELLIPTIC CURVES
DC.creator	Jeong, Keunyoung
	Park, Junyeong
	Yhee, Donggeon
DC.publisher	Osaka University and Osaka Metropolitan University, Departments of Mathematics
DC.language' scheme='DCTERMS.RFC1766	英語
DC.type' scheme='DCTERMS.DCMIType	text
DCTERMS.issued' scheme='DCTERMS.W3CDTF	2023-01
DCTERMS.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.
DC.identifier	10.18910/89992
DC.format	89992
citation_title	ON THE JACOBIAN OF A FAMILY OF HYPERELLIPTIC CURVES
citation_author	Jeong, Keunyoung
	Park, Junyeong
	Yhee, Donggeon
citation_publisher	Osaka University and Osaka Metropolitan University, Departments of Mathematics
citation_language	英語
citation_date	2023-01
citation_journal_title	Osaka Journal of Mathematics
citation_volume	60
citation_issue	1
citation_firstpage	43
citation_lastpage	60
citation_public_url	https://hdl.handle.net/11094/89992
citation_doi_detail	10.18910/89992
citation_doi	https://doi.org/10.18910/89992