{"created":"2023-07-27T06:44:30.759538+00:00","id":34763,"links":{},"metadata":{"_buckets":{"deposit":"abcc069c-c73c-4889-915f-0a31e94fbc92"},"_deposit":{"created_by":3,"id":"34763","owners":[3],"pid":{"revision_id":0,"type":"depid","value":"34763"},"status":"published"},"_oai":{"id":"oai:kanazawa-u.repo.nii.ac.jp:00034763","sets":["2812:2813:2828"]},"author_link":["93526","38"],"item_9_biblio_info_8":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2006-05-01","bibliographicIssueDateType":"Issued"},"bibliographicPageStart":"5p.","bibliographicVolumeNumber":"2002-2005","bibliographic_titles":[{"bibliographic_title":"平成17(2005)年度科学研究費補助金 基盤研究(B) 研究報告書"},{"bibliographic_title":"2005 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.新谷関数・L関数の構成 四元数歪エルミート形式のユニタリ群について,局所新谷関数の考察を行った.また,L関数のRankin-Selberg型積分表示に現れるEisenstein級数の関数等式を明示的に求めた. 2.3次ユニタリ群上の保型形式(村瀬篤氏との共同研究) (1)Kudla liftのFourier-Jacobi展開について U(1,1)上の正則尖点形式fからU(2,1)上の正則尖点形式L(f)へのKudla liftの詳細な研究を行い,L(f)の原始的テータ関数による展開を求めた.この応用として,L(f)が消えないための条件がfのU(1)周期の言葉で記述される. (2)Siegel-Weil formula U(2,1)とU(2,2)の組に関するSiegel-Weil formulaを求めた.正規化は不要であるが,かなり精密な議論を必要とする. (3)Inner product formula Kudla liftに関する内積公式を得た.fとL(f)のPetersson内積の比<L(f),L(f)>/<f,f>はfのL関数の1での値と分岐素点における局所的な量で記述される.これは,L(f)が消えないための(1)とは別種の判定条件を与えている. 3.Jacobi形式からのKudla lift Kudla liftをJacobi形式からのテータリフトと認識する立場からの研究を行った.虚2次体の類数が1の場合に,Jacobi Hecke環の同時固有関数が,3次ユニタリ群のHecke固有関数となることを示した.また,Jacob形式からのリフトを用い,保型形式環の構造に関するResnikoff-Taiの結果(ガウス数体の場合)の簡明な別証を与えた.","subitem_description_type":"Abstract"},{"subitem_description":"1.Sintani functions and construction of L-functions\nWe investigated local Shintani functions on the unitary groups of quaternion skew hermitian forms. Moreover, to construct automorphic L-functions, we calculated a functional equation of Eisenstein series explicitly.\n2.Automorphic forms on unitary groups of degree three (joint work with A.Murase)\n(1)Fourier-Jacobi expansion of Kudla lift : Let f be a holomorphic cusp form on U(1,1). S.Kudla constructed a holomorphic cusp form L(f) on U(2,1). We obtained a refined Fourier-Jacobi expansion of L(f) by primitive theta functions. As an application, we gave a criterion for non-vanishing of L(f) in terms of U(1)-period of f.\n(2)Siegel-Weil formula : We proved Siegel-Weil formula for the pair ((U(2,1),U(2,2)). We do not need regularization process.\n(3)Inner product formula : The ratio <L(f),L(f)>/<f,f> of Petersson inner prodects of L(f) and f is calculated. It is written by the special value L(f;1) and local data at ramified primes. Consequently we gave another criterion for the non-vanising of L(f).\n3.Kudla lift from Jacobi forms\nWe considered Kudla lift as a lifting from Jacobi forms to U(2,1). When the calss number of the quadratic number fields is one, it is compatible with Jacobi Hecke action. As an application of Jacobi form version, we gave another simple proof of Resnikoff-Tai's result on the structure of thegraded algebra of automorphic forms on SU(2,1) in Gaussian field case.","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:14340006, 研究期間(年度):2002–2005","subitem_description_type":"Other"},{"subitem_description":"出典：「保型形式・保型L関数・新谷関数の研究」研究成果報告書　課題番号14340006\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":"10.24517/00034750","subitem_identifier_reg_type":"JaLC"}]},"item_9_publisher_17":{"attribute_name":"公開者","attribute_value_mlt":[{"subitem_publisher":"金沢大学自然科学研究科"}]},"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-14340006/","subitem_relation_type_select":"URI"}},{"subitem_relation_type_id":{"subitem_relation_type_id_text":"https://kaken.nii.ac.jp/report/KAKENHI-PROJECT-14340006/143400062005kenkyu_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 2006-5p.pdf","filesize":[{"value":"220.0 kB"}],"format":"application/pdf","licensetype":"license_11","mimetype":"application/pdf","url":{"label":"SC-PR-SUGANO-T-kaken 2006-5p.pdf","url":"https://kanazawa-u.repo.nii.ac.jp/record/34763/files/SC-PR-SUGANO-T-kaken 2006-5p.pdf"},"version_id":"0b39e675-6e5f-42f9-9965-cf860f726523"}]},"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":"保型形式・保型L関数・新谷関数の研究","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"保型形式・保型L関数・新谷関数の研究"},{"subitem_title":"Study on automorphic forms, automorphic L-functions and Shintani functions","subitem_title_language":"en"}]},"item_type_id":"9","owner":"3","path":["2828"],"pubdate":{"attribute_name":"公開日","attribute_value":"2017-10-05"},"publish_date":"2017-10-05","publish_status":"0","recid":"34763","relation_version_is_last":true,"title":["保型形式・保型L関数・新谷関数の研究"],"weko_creator_id":"3","weko_shared_id":3},"updated":"2023-07-27T14:32:10.002151+00:00"}