{"created":"2023-07-27T06:44:34.992050+00:00","id":34859,"links":{},"metadata":{"_buckets":{"deposit":"0f7b4770-a00c-4436-835b-e6686a2f370e"},"_deposit":{"created_by":3,"id":"34859","owners":[3],"pid":{"revision_id":0,"type":"depid","value":"34859"},"status":"published"},"_oai":{"id":"oai:kanazawa-u.repo.nii.ac.jp:00034859","sets":["2812:2813:2835"]},"author_link":["93526","38"],"item_9_biblio_info_8":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"1999-03-01","bibliographicIssueDateType":"Issued"},"bibliographicPageStart":"3p.","bibliographicVolumeNumber":"1997-1998","bibliographic_titles":[{"bibliographic_title":"平成10(1998)年度 科学研究費補助金 基盤研究(C) 研究成果報告書"},{"bibliographic_title":"1998 Fiscal Year Final Research Report","bibliographic_titleLang":"en"}]}]},"item_9_creator_33":{"attribute_name":"著者別表示","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{}],"nameIdentifiers":[{},{}]}]},"item_9_description_21":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"1. ユニタリ群の保型L関数について(村瀬駕氏との共同研究) 一般符号のユニタリ群上の正則尖点形式に付随する標準的L関数について、その解析接続・関数等式を証明した。証明の鍵は、新谷関数とその積分の研究である。技術的条件下では既に我々自身によって得られていたが、局所・大域の両面に渡る議論の精密化により、この条件を取り除くことに成功した。 2. 3次ユニタリ群上の保型形式とテータ関数について(村瀬篤氏との共同研究) 3次ユニタリ群上の正則保型形式の数論的研究においては、新谷卓郎氏により導入された「原始的テータ関数」が重要な役割を果たす。テータ関数の空間を純局所的に定式化し、Weil表現のlattice model及びtrace formulaを用いて詳しく考察した。原始的テータ関数の空間に現れる、二次拡大の乗法群の指標を完全に決定し、epsilon factorを用いて記述した。また、大域的保型形式への応用として、正則Eisenstein級数の、原始的テータ関数での展開係数を決定した(L関数の特殊値により記述される)。 3. theta lift・Jacobi型群(村瀬篤氏との共同研究) 楕円保型形式から3次ユニタリ群上の保型形式Kudla liftは、直交群0(2,4)へのOda liftの制限と完全に一致し、従ってJacobi形式からのliftと見なされる。この立場から、具体的なJacobi形式の像を考察。また、前項で述べた正則Eisenstein級数の展開を、Jacobi型群上の新谷関数の言葉を用いた解釈を与えた。","subitem_description_type":"Abstract"},{"subitem_description":"1. Automorphic L-functions on unitary groups (joint work with A.Murase)\nWe poved the analytic continuation and the functional equations of the standard L-function associated with a holomorphic cusp form on a unitary group. The key ingredient in the proof is a study of Shintani functions.\n2. Automorphic forms on unitary groups of degree 3 and primitive theta functions (joint work with A.Murase)\nFor the study of arithmetical automorphic forms on a unitary group of degree 3, primitive theta functions are fundamental. We investigated a metaplectic representation of U(1) acting on the space of local primitive theta functions and gave its explicit irreducible decomposition.\nAs an application, we determined the refined Fourier-Jacobi expansion of holomorphic Eisenstein series.\n3. theta lift and Jacobi group (joint work with A.Murase)\nSince Kudla lift is a restriction of Oda lift, we can construct automorphic forms on unitary groups of degree 3 from Jacobi forms explicitly. We gave another formulation of refined Fourier-Jacobi expansion of holomorphic Eisenstein series using Jacobi type Eisenstein series.","subitem_description_type":"Abstract"}]},"item_9_description_22":{"attribute_name":"内容記述","attribute_value_mlt":[{"subitem_description":"研究課題/領域番号:09640040, 研究期間(年度):1997–1998","subitem_description_type":"Other"},{"subitem_description":"出典：「代数群上の保型形式とL関数」研究成果報告書　課題番号09640040\n  (KAKEN：科学研究費助成事業データベース（国立情報学研究所）)\n　　　本文データは著者版報告書より作成","subitem_description_type":"Other"}]},"item_9_identifier_registration":{"attribute_name":"ID登録","attribute_value_mlt":[{"subitem_identifier_reg_text":"10.24517/00034846","subitem_identifier_reg_type":"JaLC"}]},"item_9_publisher_17":{"attribute_name":"公開者","attribute_value_mlt":[{"subitem_publisher":"金沢大学理学部"}]},"item_9_relation_28":{"attribute_name":"関連URI","attribute_value_mlt":[{"subitem_relation_type_id":{"subitem_relation_type_id_text":"https://kaken.nii.ac.jp/search/?qm=30183841","subitem_relation_type_select":"URI"}},{"subitem_relation_type_id":{"subitem_relation_type_id_text":"https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640040/","subitem_relation_type_select":"URI"}},{"subitem_relation_type_id":{"subitem_relation_type_id_text":"https://kaken.nii.ac.jp/report/KAKENHI-PROJECT-09640040/096400401998kenkyu_seika_hokoku_gaiyo/","subitem_relation_type_select":"URI"}}]},"item_9_version_type_25":{"attribute_name":"著者版フラグ","attribute_value_mlt":[{"subitem_version_resource":"http://purl.org/coar/version/c_ab4af688f83e57aa","subitem_version_type":"AM"}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2017-10-05"}],"displaytype":"detail","filename":"SC-PR-SUGANO-T-kaken 1999-3p.pdf","filesize":[{"value":"76.4 kB"}],"format":"application/pdf","licensetype":"license_11","mimetype":"application/pdf","url":{"label":"SC-PR-SUGANO-T-kaken 1999-3p.pdf","url":"https://kanazawa-u.repo.nii.ac.jp/record/34859/files/SC-PR-SUGANO-T-kaken 1999-3p.pdf"},"version_id":"39b1c323-0e81-4274-b19c-95d874a93348"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"jpn"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"research report","resourceuri":"http://purl.org/coar/resource_type/c_18ws"}]},"item_title":"代数群上の保型形式とL関数","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"代数群上の保型形式とL関数"},{"subitem_title":"Automorphic forms and L functions on algebraic groups","subitem_title_language":"en"}]},"item_type_id":"9","owner":"3","path":["2835"],"pubdate":{"attribute_name":"公開日","attribute_value":"2017-10-05"},"publish_date":"2017-10-05","publish_status":"0","recid":"34859","relation_version_is_last":true,"title":["代数群上の保型形式とL関数"],"weko_creator_id":"3","weko_shared_id":3},"updated":"2023-07-27T14:47:02.799519+00:00"}