THE ORBITS OF PRIMITIVE REPRESENTATIONS OF A QUADRATIC FORM BY A QUADRATIC FORM

Murata, Manabu

Osaka Journal of Mathematics, 2026, 63(1), 91-110

アクセス数:15件（2026-04-05 11:44 集計）

固定URL: https://doi.org/10.18910/103806

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タイトル	THE ORBITS OF PRIMITIVE REPRESENTATIONS OF A QUADRATIC FORM BY A QUADRATIC FORM
著者	著者名 Murata, Manabu
抄録	We study the primitive integral representations of a quadratic form in n − 1 variables by a reduced quadratic form in n variables. Our aim is to describe the orbits of such representations under the action of the unit group of the reduced form. That description provides the mass of the representations, considered by Shimura. A formula for computation of the mass is also proved in the indefinite case.
出版者	Departments of Mathematics, The University of Osaka and Osaka Metropolitan University
収録物名	Osaka Journal of Mathematics
巻(号)	63(1)
ページ	91-110
刊行年月	2026-01
言語	英語
ハンドルURL	https://hdl.handle.net/11094/103806
DOI	https://doi.org/10.18910/103806
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 63, Number 1 （2026-01)

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. 2026, 63(1), p. 91-110
DC.title	THE ORBITS OF PRIMITIVE REPRESENTATIONS OF A QUADRATIC FORM BY A QUADRATIC FORM
DC.creator	Murata, Manabu
DC.publisher	Departments of Mathematics, The University of Osaka and Osaka Metropolitan University
DC.language' scheme='DCTERMS.RFC1766	英語
DC.type' scheme='DCTERMS.DCMIType	text
DCTERMS.issued' scheme='DCTERMS.W3CDTF	2026-01
DCTERMS.abstract	We study the primitive integral representations of a quadratic form in n − 1 variables by a reduced quadratic form in n variables. Our aim is to describe the orbits of such representations under the action of the unit group of the reduced form. That description provides the mass of the representations, considered by Shimura. A formula for computation of the mass is also proved in the indefinite case.
DC.identifier	10.18910/103806
DC.format	103806
citation_title	THE ORBITS OF PRIMITIVE REPRESENTATIONS OF A QUADRATIC FORM BY A QUADRATIC FORM
citation_author	Murata, Manabu
citation_publisher	Departments of Mathematics, The University of Osaka and Osaka Metropolitan University
citation_language	英語
citation_date	2026-01
citation_journal_title	Osaka Journal of Mathematics
citation_volume	63
citation_issue	1
citation_firstpage	91
citation_lastpage	110
citation_public_url	https://hdl.handle.net/11094/103806
citation_doi_detail	10.18910/103806
citation_doi	https://doi.org/10.18910/103806