On the class numbers of certain number fields obtained from points on elliptic curves II

Sato, Atsuhi

Osaka Journal of Mathematics, 2008, 45(2), 375-390

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固定URL: https://doi.org/10.18910/4092

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タイトル	On the class numbers of certain number fields obtained from points on elliptic curves II
著者	著者名 Sato, Atsuhi
抄録	We construct a family of cyclic extensions of number fields, in which every finite place is unramified, from an elliptic curve with a rational torsion point. As an application, we obtain such polynomials F(X) of rational coefficients that have the following property: For a rational number ξ chosen at random, the class number of the field generated by the square root of F(ξ) is “often” divisible by 3, 5 or by 7.
出版者	Osaka University and Osaka City University, Departments of Mathematics
収録物名	Osaka Journal of Mathematics
巻(号)	45(2)
ページ	375-390
刊行年月	2008-06
言語	英語
ハンドルURL	https://hdl.handle.net/11094/4092
DOI	https://doi.org/10.18910/4092
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 45, Number 2　(2008）

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
作成日	2008-06
DCTERMS.bibliographicCitation	Osaka Journal of Mathematics. 2008, 45(2), p. 375-390
DC.title	On the class numbers of certain number fields obtained from points on elliptic curves II
DC.creator	Sato, Atsuhi
DC.publisher	Osaka University and Osaka City University, Departments of Mathematics
DC.language' scheme='DCTERMS.RFC1766	英語
DC.type' scheme='DCTERMS.DCMIType	text
DCTERMS.issued' scheme='DCTERMS.W3CDTF	2008-06
DCTERMS.abstract	We construct a family of cyclic extensions of number fields, in which every finite place is unramified, from an elliptic curve with a rational torsion point. As an application, we obtain such polynomials F(X) of rational coefficients that have the following property: For a rational number ξ chosen at random, the class number of the field generated by the square root of F(ξ) is “often” divisible by 3, 5 or by 7.
DC.identifier	10.18910/4092
DC.format	4092
citation_title	On the class numbers of certain number fields obtained from points on elliptic curves II
citation_author	Sato, Atsuhi
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2008-06
citation_journal_title	Osaka Journal of Mathematics
citation_volume	45
citation_issue	2
citation_firstpage	375
citation_lastpage	390
citation_public_url	https://hdl.handle.net/11094/4092
citation_doi_detail	10.18910/4092
citation_doi	https://doi.org/10.18910/4092