{"created":"2023-06-20T16:34:02.921890+00:00","id":3130,"links":{},"metadata":{"_buckets":{"deposit":"ed3bc840-aa6f-45c9-b6e9-9506ffca0317"},"_deposit":{"created_by":3,"id":"3130","owners":[3],"pid":{"revision_id":0,"type":"depid","value":"3130"},"status":"published"},"_oai":{"id":"oai:kindai.repo.nii.ac.jp:00003130","sets":["14:2667:2689:2693","21:2669:2691:2694"]},"author_link":["3460"],"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":"Number theoretic and coding theoretic study of zeta functions appearing in applied mathematics"}]},"item_8_biblio_info_21":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2010-01-01","bibliographicIssueDateType":"Issued"},"bibliographicPageEnd":"4","bibliographicPageStart":"1","bibliographic_titles":[{"bibliographic_title":"科学研究費補助金研究成果報告書 (2010. )"}]}]},"item_8_description_33":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"研究成果の概要（和文）：本研究で取り扱ったのは、符号のゼータ関数の理論の拡張である。考察の対象をマクウイリアムズ変換で不変なすべての多項式にまで広げた。さらに、実在の自己双対でない符号から、大量の不変式を系統的に作り出す方法を導入した。この方法を用いて、いくつかの有名な線型符号の系列から得られた不変式のリーマン予想を考察した。それらはMDS 符号、一般ハミング符号、非自己双対ゴレイ符号である。これらの一部は「完全符号」という族を形成する。われわれは、一般ハミング符号の一部の系列を除いて、これらの不変式がリーマン予想を満たすことを証明できた。       研究成果の概要（英文）：This project dealt with a generalization of the theory of zeta functions for linear codes. We extended the consideration to all the polynomials which were invariant under the MacWilliams transform. Moreover we introduced a method to produce many invariant polynomials systematically from the existing codes which were not self-dual. Using this method, we considered the Riemann hypothesis for invariant polynomials which were obtained from some famous families of linear codes. They were the MDS codes, general Hamming codes and non-self-dual Golay codes. Some of them form a family “perfect codes”. We could prove that, except for some sequences of the general Hamming codes, their invariant polynomials satisfied the Riemann hypothesis.","subitem_description_type":"Abstract"}]},"item_8_description_36":{"attribute_name":"内容記述","attribute_value_mlt":[{"subitem_description":"研究種目：基盤研究 (C);  研究期間：2008～2010;   課題番号：20540032;   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/ja/r/30419486"}]}]},"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":"CHINEN, KOJI"}]},"item_8_text_8":{"attribute_name":"著者 所属","attribute_value_mlt":[{"subitem_text_value":"近畿大学理工学部; 准教授"}]},"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":"知念,  宏司"},{"creatorName":"チネン, コウジ","creatorNameLang":"ja-Kana"}],"nameIdentifiers":[{"nameIdentifier":"3460","nameIdentifierScheme":"WEKO"},{"nameIdentifier":"30419486","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_20540032seika.pdf","filesize":[{"value":"328.3 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"KAKEN_20540032seika.pdf","url":"https://kindai.repo.nii.ac.jp/record/3130/files/KAKEN_20540032seika.pdf"},"version_id":"76483dcf-e526-411f-a082-602299645975"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"線型符号","subitem_subject_scheme":"Other"},{"subitem_subject":"完全符号","subitem_subject_scheme":"Other"},{"subitem_subject":"ゼータ関数","subitem_subject_scheme":"Other"},{"subitem_subject":"不変式環","subitem_subject_scheme":"Other"},{"subitem_subject":"リーマン予想","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":"応用数学に現れるゼータ関数の数論的および符号理論的研究","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"応用数学に現れるゼータ関数の数論的および符号理論的研究"}]},"item_type_id":"8","owner":"3","path":["2693","2694"],"pubdate":{"attribute_name":"公開日","attribute_value":"2011-07-08"},"publish_date":"2011-07-08","publish_status":"0","recid":"3130","relation_version_is_last":true,"title":["応用数学に現れるゼータ関数の数論的および符号理論的研究"],"weko_creator_id":"3","weko_shared_id":-1},"updated":"2023-06-21T01:45:41.694978+00:00"}