{"created":"2023-06-20T16:34:02.964039+00:00","id":3131,"links":{},"metadata":{"_buckets":{"deposit":"9a3ae4c3-39fb-4496-b984-4c3e41a3eb47"},"_deposit":{"created_by":3,"id":"3131","owners":[3],"pid":{"revision_id":0,"type":"depid","value":"3131"},"status":"published"},"_oai":{"id":"oai:kindai.repo.nii.ac.jp:00003131","sets":["14:2667:2689:2693","21:2669:2691:2694"]},"author_link":["3461","3462"],"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":"A study of zeta functions of prehomogeneous vector spaces and multiple zeta values"}]},"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）： 概均質ベクトル空間については、２元３次形式の空間における、有理整数環に関するすべての格子に付随するゼータ関数に対して、それらの間に成り立つ代数的関係式の解明を完成した。この事実はこの対象の判別式が正の部分と負の部分の間に未解明な対称性が存在することを示唆しており興味深い。多重ゼータ値環については、多重ゼータ値と等号付き多重ゼータ値の間の関係を解明し、ホフマンによる予想基底を用いて正の整数点におけるリーマンゼータ値を記述した。また、重さ・深さ・i-高さを固定した等号付き多重ゼータ値の和について、一般超幾何関数を用いた母関数表示の公式を与えた。また、高さ１の等号付き多重ゼータ値のある種の双対公式も証明した。さらに、多重ゼータ値の新たな和公式の一般化など多数の成果を得た。これらの結果は多重ゼータ値の張る有理数体上の環の構造解明のため重要である。    研究成果の概要（英文）： We figured out algebraic relations among the zeta functions of the prehomogeneous vector space associated with binary cubic forms with all lattices over the integer ring. These relations suggest the existence of beautiful symmetries of these objects, which are not yet known. We also clarified the relation among multiple zeta values and multiple zeta-star values, and figured out the explicit formula of Riemann zeta values of positive integral points in terms of multiple zeta-star analogue of Michael Hoffman’s conjectural basis. Moreover we obtain a generating function representation of totals of multiple zeta-star values of fixed weight, depth and i-heights in terms of generalized hypergeometric functions. We also gave a kind of duality formula for multiple zeta-star values of height one. Farther we obtained another generalization of sum formula for multiple zeta values and many related results. These results are important for understanding the structure of Q-algebra spanned by all multiple zeta values.","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：20540033;   研究分野：;   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/70330230"}]},{"subitem_relation_name":[{"subitem_relation_name_text":"https://kaken.nii.ac.jp/ja/r/10432121"}]}]},"item_8_text_10":{"attribute_name":"著者 役割","attribute_value_mlt":[{"subitem_text_value":"研究代表者"},{"subitem_text_value":"連携研究者"}]},"item_8_text_7":{"attribute_name":"著者(英)","attribute_value_mlt":[{"subitem_text_language":"en","subitem_text_value":"ONO, YASUO"},{"subitem_text_language":"en","subitem_text_value":"WAKATSUKI, SATOSHI"}]},"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"},{"subitem_text_value":"金沢大学数物科学系; 助教"}]},"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":"大野,  泰生"},{"creatorName":"オオノ, ヤスオ","creatorNameLang":"ja-Kana"}],"nameIdentifiers":[{"nameIdentifier":"3461","nameIdentifierScheme":"WEKO"},{"nameIdentifier":"10432121","nameIdentifierScheme":"研究者番号","nameIdentifierURI":" "}]},{"creatorNames":[{"creatorName":"若槻,  聡"},{"creatorName":"ワカツキ, サトシ","creatorNameLang":"ja-Kana"}],"nameIdentifiers":[{"nameIdentifier":"3462","nameIdentifierScheme":"WEKO"}]}]},"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_20540033seika.pdf","filesize":[{"value":"316.8 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"KAKEN_20540033seika.pdf","url":"https://kindai.repo.nii.ac.jp/record/3131/files/KAKEN_20540033seika.pdf"},"version_id":"ef46aedf-60c6-4c75-bce5-acf40a79390f"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"数論","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":"概均質ベクトル空間のゼータ関数と多重ゼータ値の研究","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"概均質ベクトル空間のゼータ関数と多重ゼータ値の研究"}]},"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":"3131","relation_version_is_last":true,"title":["概均質ベクトル空間のゼータ関数と多重ゼータ値の研究"],"weko_creator_id":"3","weko_shared_id":-1},"updated":"2023-06-21T01:45:39.634129+00:00"}