{"created":"2023-06-20T16:34:21.701321+00:00","id":3537,"links":{},"metadata":{"_buckets":{"deposit":"9dccee7e-9ad6-478c-876f-b5205875337e"},"_deposit":{"created_by":3,"id":"3537","owners":[3],"pid":{"revision_id":0,"type":"depid","value":"3537"},"status":"published"},"_oai":{"id":"oai:kindai.repo.nii.ac.jp:00003537","sets":["14:2667:2675:2679:2683","21:2669:2677:2681:2684"]},"author_link":["3336"],"item_8_alternative_title_3":{"attribute_name":"その他（別言語等）のタイトル","attribute_value_mlt":[{"subitem_alternative_title":"Study on the arithmetic theory of automorphic forms of several variables"}]},"item_8_biblio_info_21":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2012-01-01","bibliographicIssueDateType":"Issued"},"bibliographicPageEnd":"4","bibliographicPageStart":"1","bibliographic_titles":[{"bibliographic_title":"科学研究費助成事業研究成果報告書 (2012. )"}]}]},"item_8_description_33":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"研究成果の概要（和文）：  ）：一変数のモジュラー形式の場合にセールやスイナートン＝ダイヤー等が考察した「p 進理論」や「標数p」のモジュラー形式の理論を多変数のモジュラー形式、例えばジーゲルモジュラー形式やエルミートモジュラー形式の場合に拡張を試み、成果を得た。具体的に、p 進理論においてを得るという新たなモジュラー形式構成法を開発した。また、標数p 理論においては、ある虚2 次体上の2 次エルミートモジュラー形式のなす環の構造を決定した。またp 進理論の応用として一変数の場合、ラマヌジャンが発見したモジュラー形式のフーリエ係数の間に成立している合同式を、多変数のモジュラー形式の場合に拡張した。これらは一変数のモジュラー形式の単なる拡張としてのみならず、ある重さのエルミートカスプ形式が存在するという事実の発見につながった。さらにこれらの成果ジーゲルモジュラー形式の場合、ベクトル値の場合まで範囲を拡げ研究を行い、テータ作用素とよばれるモジュラー形式の微分作用素のp進的性質の解明を行った。        研究成果の概要（英文）：The p-adic theory of modular forms initiated by J.-P. Serre and H.P.F.Swinnerton-Dyer was established in the case of one variable by several people. I tried to generalize the theory to the case of several variables, for example, Siegel modular forms and Hermitian modular forms, and obtained several results. More specifically, I established a constructing method by taking a p-adic limit of a sequence of ordinary modular forms. Concerning the mod p theory, I studied the structure of the graded ring of Hermitian modular forms and determined the structure in some cases. Moreover, I generalized some congruence properties of Siegel modular forms originated with Ramanujan. This result wasapplied to show the existence of cusp forms of several variables. I studied the p-adic theory and mod p theory of modular forms of several variables and produced fruits. Moreover, the case of vector-valued was considered. In particular, the p-adic theory of the theta operator, which is a kind of differential operator on modular forms, was developed.","subitem_description_type":"Abstract"}]},"item_8_description_36":{"attribute_name":"内容記述","attribute_value_mlt":[{"subitem_description":"機関番号:34419;   研究種目：基盤研究（C）;  研究期間：2010～2012;   課題番号：22540036;   研究分野：数物系科学;   科研費の分科・細目：数学・代数学","subitem_description_type":"Other"}]},"item_8_description_37":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"subitem_description":"Research Paper","subitem_description_type":"Other"}]},"item_8_description_41":{"attribute_name":"フォーマット","attribute_value_mlt":[{"subitem_description":"application/pdf","subitem_description_type":"Other"}]},"item_8_publisher_14":{"attribute_name":"出版者 名前","attribute_value_mlt":[{"subitem_publisher":"近畿大学"}]},"item_8_relation_11":{"attribute_name":"著者 外部リンク","attribute_value_mlt":[{"subitem_relation_name":[{"subitem_relation_name_text":"https://kaken.nii.ac.jp/d/r/20164402.ja.html"}]}]},"item_8_text_10":{"attribute_name":"著者 役割","attribute_value_mlt":[{"subitem_text_value":"研究代表者"}]},"item_8_text_7":{"attribute_name":"著者(英)","attribute_value_mlt":[{"subitem_text_language":"en","subitem_text_value":"NAGAOKA, SHOYU"}]},"item_8_text_8":{"attribute_name":"著者 所属","attribute_value_mlt":[{"subitem_text_value":"近畿大学理工学部; 教授"}]},"item_8_text_9":{"attribute_name":"著者所属(翻訳)","attribute_value_mlt":[{"subitem_text_value":"Kinki University"}]},"item_8_version_type_12":{"attribute_name":"版","attribute_value_mlt":[{"subitem_version_resource":"http://purl.org/coar/version/c_970fb48d4fbd8a85","subitem_version_type":"VoR"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"長岡,  昇勇"},{"creatorName":"ナガオカ, ショウユウ","creatorNameLang":"ja-Kana"}],"nameIdentifiers":[{"nameIdentifier":"3336","nameIdentifierScheme":"WEKO"},{"nameIdentifier":"20164402","nameIdentifierScheme":"研究者番号","nameIdentifierURI":" "}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2016-02-17"}],"displaytype":"detail","filename":"KAKEN_22540036seika.pdf","filesize":[{"value":"193.5 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"KAKEN_22540036seika.pdf","url":"https://kindai.repo.nii.ac.jp/record/3537/files/KAKEN_22540036seika.pdf"},"version_id":"43f929b3-5c28-486e-89a7-66e4e2da6a34"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"整数論","subitem_subject_scheme":"Other"},{"subitem_subject":"保型形式","subitem_subject_scheme":"Other"},{"subitem_subject":"p進理論","subitem_subject_scheme":"Other"}]},"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":"多変数保型形式の整数論的研究","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"多変数保型形式の整数論的研究"}]},"item_type_id":"8","owner":"3","path":["2683","2684"],"pubdate":{"attribute_name":"公開日","attribute_value":"2013-07-25"},"publish_date":"2013-07-25","publish_status":"0","recid":"3537","relation_version_is_last":true,"title":["多変数保型形式の整数論的研究"],"weko_creator_id":"3","weko_shared_id":-1},"updated":"2023-06-21T01:32:18.403832+00:00"}