CLASS NUMBER PARITY OF A QUADRATIC TWIST OF A CYCLOTOMIC FIELD OF PRIME POWER CONDUCTOR

Ichimura, Humio

doi:https://doi.org/10.18910/25091

アクセス数:116件（2024-05-13 09:06 集計）

固定URL: https://doi.org/10.18910/25091

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タイトル	CLASS NUMBER PARITY OF A QUADRATIC TWIST OF A CYCLOTOMIC FIELD OF PRIME POWER CONDUCTOR
著者	NRID 1000000203109 1000000203109 著者名 Ichimura, Humio
抄録	Let p be a fixed odd prime number and K_n the p^<n+1>-st cyclotomic field. For a fixed integer d∊Z with √<d>∉K_0, denote by L_n the imaginary quadratic subextension of the biquadratic extension K_n(√<d>)/K_n^+ with L_n≠K_n. Let h^* _n and h^-_n be the relative class numbers of K_n and L_n, respectively. We give an explicit constant nd depending on p and d such that (i) for any integer n≥n_d , the ratio h^-_n/h^-_<n+1> is odd if and only if h^_n =h^_<n-1> is odd and (ii) for 1≤n<n_d , h^-_n/h^-_<n-1> is even.
出版者	Osaka University and Osaka City University, Departments of Mathematics
収録物名	Osaka Journal of Mathematics
巻(号)	50(2)
ページ	563-572
刊行年月	2013-06
言語	英語
ハンドルURL	https://hdl.handle.net/11094/25091
DOI	https://doi.org/10.18910/25091
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 50, Number 2　(2013-6）

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. 2013, 50(2), p. 563-572
DC.title	CLASS NUMBER PARITY OF A QUADRATIC TWIST OF A CYCLOTOMIC FIELD OF PRIME POWER CONDUCTOR
DC.creator	Ichimura, Humio
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	2013-06
DCTERMS.abstract	Let p be a fixed odd prime number and K_n the p^<n+1>-st cyclotomic field. For a fixed integer d∊Z with √<d>∉K_0, denote by L_n the imaginary quadratic subextension of the biquadratic extension K_n(√<d>)/K_n^+ with L_n≠K_n. Let h^* _n and h^-_n be the relative class numbers of K_n and L_n, respectively. We give an explicit constant nd depending on p and d such that (i) for any integer n≥n_d , the ratio h^-_n/h^-_<n+1> is odd if and only if h^_n =h^_<n-1> is odd and (ii) for 1≤n<n_d , h^-_n/h^-_<n-1> is even.
DC.identifier	10.18910/25091
DC.format	application/pdf
citation_title	CLASS NUMBER PARITY OF A QUADRATIC TWIST OF A CYCLOTOMIC FIELD OF PRIME POWER CONDUCTOR
citation_author	Ichimura, Humio
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2013-06
citation_journal_title	Osaka Journal of Mathematics
citation_volume	50
citation_issue	2
citation_firstpage	563
citation_lastpage	572
citation_public_url	https://hdl.handle.net/11094/25091
citation_doi_detail	10.18910/25091
citation_doi	https://doi.org/10.18910/25091

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