{"created":"2022-01-27T08:04:29.122990+00:00","id":2004426,"links":{},"metadata":{"_buckets":{"deposit":"81df24d3-f131-47e2-8bf3-8955cf0eaae2"},"_deposit":{"id":"2004426","owners":[1],"pid":{"revision_id":0,"type":"depid","value":"2004426"},"status":"published"},"_oai":{"id":"oai:u-ryukyu.repo.nii.ac.jp:02004426","sets":["1642838403123","1642838403551:1642838405037"]},"author_link":[],"item_1617186331708":{"attribute_name":"Title","attribute_value_mlt":[{"subitem_1551255647225":"有限モノドロミー群をもつ超幾何微分方程式の Schwarz map","subitem_1551255648112":"ja"},{"subitem_1551255647225":"Schwarz maps of hypergeometric differential equations with finite monodromy groups","subitem_1551255648112":"en"}]},"item_1617186419668":{"attribute_name":"Creator","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"加藤, 満生","creatorNameLang":"ja"}]},{"creatorNames":[{"creatorName":"Kato, Mitsuo","creatorNameLang":"en"}]}]},"item_1617186476635":{"attribute_name":"Access Rights","attribute_value_mlt":[{"subitem_1522299639480":"open access","subitem_1600958577026":"http://purl.org/coar/access_right/c_abf2"}]},"item_1617186609386":{"attribute_name":"Subject","attribute_value_mlt":[{"subitem_1522299896455":"en","subitem_1522300014469":"Other","subitem_1523261968819":"hypergeometric function"},{"subitem_1522299896455":"en","subitem_1522300014469":"Other","subitem_1523261968819":"monodromy group"},{"subitem_1522299896455":"en","subitem_1522300014469":"Other","subitem_1523261968819":"Schwarz map"}]},"item_1617186626617":{"attribute_name":"Description","attribute_value_mlt":[{"subitem_description":"科研費番号: 12640031","subitem_description_type":"Other"},{"subitem_description":"平成12年度～平成13年度  科学研究費補助金基盤研究(C)(2)研究成果報告書 / 研究概要 : Gaussの超幾何微分方程式の拡張として一般型、_<n+1>F_n, Appell型F_1,F_2,F_3,F_4,(k,n)型超幾何微分方程式等がある。本研究では,主にAppell F_2とimprimitiveな_<n+1>F_nに対して以下の研究を行った.1)有限既約なモノドロミー群をもつAppell F_2を決定した.その条件はF_2がもつ5個のパラメータによって言い表され,本質的に6種類に分類される.そのいずれの場合もモノドロミー群は簡単な可換群とunitary reflection groupとの半直積になっている.そこに現れるreflection groupはShephard-Toddの分類表のimprimitiveなG(2,2,4)とprimitiveなNo.28,30,32の群である. No.30の群は2種のモノドロミー群に現れるが,そこでの可換群が異なっている.6種のモノドロミー群のうち5つは4つの1次独立な解の間に2次関係式が存在する.残りの1つ,No.32のunitary groupをふくむモノドロミー群を持つ微分方程式のSchwarz mapの像はP^3内の90次曲面となる。2)Imprimitiveな有限モノドロミー群をもつ、_nF_<n-1>の Schwarz mapのmapの像Cは方程式y^<mn>+xy^<mq>-1=0の1次独立なn個の解の比で決まるP^<n- 1>内の点の(xを動かしたときの)軌跡となる.上の3項n次方程式の解はx=0で正則な関数で一般型2項関数とも呼ばれ、本研究に重要な役割を果す。特に_3F_2とy^3+xy-1=0の関係を考察することにより、3次方程式のカルダノの公式の別証明が得られる。","subitem_description_type":"Other"},{"subitem_description":"Appell's hypergeometric function F_2(a; b, b'; c, c'; x, y) =Σ^^∞_<m,n=0>((a,m+n)(b,m)(b',n))/((c,m)(c',n)(1,m)(1,n))x^my^n, where(a,n) = Γ(a+n)/Γ(a), satisfies a system E_2(a;b,b';c,c') of differential equations on the (x,y)-space X (【similar or equal】P^2). 1. I tabulated all the systems of parameters (a;b,b';c,c') into six classes such that each E_2(a;b,b';c,c') has a finite irreducible monodromy group. These monodromy groups have reflection subgroups whose Shephard-Todd numbers are 2,28,30 and 32. 2. The system E: = E_2(-1/<12>;1/6;1/<12>;1/3;1/2) has the biggest finite irreducible monodromy group G of order 12・25920. A Schwarz map s_E of E defined by the ratio of four linearly independent solutions of E is a 25920-valued map of X-Sing(E) into P^3, where Sing(E) denotes the singular locus of E. The closure S of the image of s_E turns out to be an irreducible hypersurface of degree 90 on which G acts.","subitem_description_type":"Other"},{"subitem_description":"研究報告書","subitem_description_type":"Other"}]},"item_1617186643794":{"attribute_name":"Publisher","attribute_value_mlt":[{"subitem_1522300295150":"ja","subitem_1522300316516":"加藤満生"}]},"item_1617186702042":{"attribute_name":"Language","attribute_value_mlt":[{"subitem_1551255818386":"eng"}]},"item_1617186783814":{"attribute_name":"Identifier","attribute_value_mlt":[{"subitem_identifier_type":"HDL","subitem_identifier_uri":"http://hdl.handle.net/20.500.12000/8947"}]},"item_1617186920753":{"attribute_name":"Source Identifier","attribute_value_mlt":[{"subitem_1522646500366":"NCID","subitem_1522646572813":"BA6427974X"}]},"item_1617187056579":{"attribute_name":"Bibliographic Information","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2002-03","bibliographicIssueDateType":"Issued"},"bibliographicPageStart":"none"}]},"item_1617258105262":{"attribute_name":"Resource Type","attribute_value_mlt":[{"resourcetype":"research report","resourceuri":"http://purl.org/coar/resource_type/c_18ws"}]},"item_1617265215918":{"attribute_name":"Version Type","attribute_value_mlt":[{"subitem_1522305645492":"VoR","subitem_1600292170262":"http://purl.org/coar/version/c_970fb48d4fbd8a85"}]},"item_1617605131499":{"attribute_name":"File","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_access","filename":"kato_m01-5.pdf","mimetype":"application/pdf","url":{"objectType":"fulltext","url":"https://u-ryukyu.repo.nii.ac.jp/record/2004426/files/kato_m01-5.pdf"},"version_id":"6e5451cf-c3ef-45f9-835d-a1997ffd701b"},{"accessrole":"open_access","filename":"kato_m01-4.pdf","mimetype":"application/pdf","url":{"objectType":"fulltext","url":"https://u-ryukyu.repo.nii.ac.jp/record/2004426/files/kato_m01-4.pdf"},"version_id":"b6a2296f-0cb7-4d45-8caf-a98c26f03792"},{"accessrole":"open_access","filename":"kato_m01-3.pdf","mimetype":"application/pdf","url":{"objectType":"fulltext","url":"https://u-ryukyu.repo.nii.ac.jp/record/2004426/files/kato_m01-3.pdf"},"version_id":"faa09ac9-9795-42c6-bdde-2b0aed8004f2"},{"accessrole":"open_access","filename":"kato_m01-2.pdf","mimetype":"application/pdf","url":{"objectType":"fulltext","url":"https://u-ryukyu.repo.nii.ac.jp/record/2004426/files/kato_m01-2.pdf"},"version_id":"3e5d9315-45ac-421b-9f63-b57393dcd39f"},{"accessrole":"open_access","filename":"kato_m01-1.pdf","mimetype":"application/pdf","url":{"objectType":"fulltext","url":"https://u-ryukyu.repo.nii.ac.jp/record/2004426/files/kato_m01-1.pdf"},"version_id":"60d6acba-f278-4e39-8306-163a5be663cb"}]},"item_title":"有限モノドロミー群をもつ超幾何微分方程式の Schwarz map","item_type_id":"15","owner":"1","path":["1642838403123","1642838405037"],"pubdate":{"attribute_name":"PubDate","attribute_value":"2009-02-27"},"publish_date":"2009-02-27","publish_status":"0","recid":"2004426","relation_version_is_last":true,"title":["有限モノドロミー群をもつ超幾何微分方程式の Schwarz map"],"weko_creator_id":"1","weko_shared_id":-1},"updated":"2022-10-31T01:57:11.532085+00:00"}