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NAKAHARA Toru  中原 徹

ORCIDConnect your ORCID iD *help
… Alternative Names

MORI Toru

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Researcher Number 50039278
External Links
Affiliation (based on the past Project Information) *help 2010: Saga University, 佐賀大学, 名誉教授
2008 – 2010: Saga University, 名誉教授
1995 – 2007: 佐賀大学, 理工学部, 教授
1987 – 1993: 佐賀大学, 理工学部, 教授
1988: Saga University, Faculty of Science and Engineering; Professor
1986: 佐賀大学, 理工学部, 教綬
Review Section/Research Field
Principal Investigator
Algebra / Algebra / 代数学・幾何学
Except Principal Investigator
Algebra / Algebra / 解析学 / 代数学・幾何学 / General mathematics (including Probability theory/Statistical mathematics)
Keywords
Principal Investigator
Hasseの問題 / 代数幾何符号 / 類数 / 整数環の巾底 / タイヒミュラー基本亜群 / エルミート符号 / Hasse's Problem / 2次体 / 保型形式 / Stanley-Reisner環 … More / 基本単数 / 巾底 / 最小距離 / Mordell Curve / 楕円曲線 / Mordell曲線 / Galois representation / Hermitian code / ディリクレの類数公式 / タイヒミュラー空間 / ファジーネス / 半線形楕円型方程式 / 代数的整数論 / 純6次体 / 頂切離散付値環 / Buchsbaum多様体 / モノミアル イデアル / 一点型代数幾何符号 / symplectic group / 分割関数 / モノミアルイデアル / 実二次体 / Bughsbaum多様体 / Cohen-Macaulay性 / Serreの保型性予想 / ガロア表現 / 射影多様体 / mod p表現 / 頂切離散附値環 / 類数の可除性 / 単数 / 類数公式 / 局所体 / chow形式 / 量子空間 / 二次体 / イデアル類群の階数評価 / 類群の構造探査へのグラフ理論の援用 / 一変数代数関数体 / Hasse-Witt行列 / 円単数とヤコビの和 / ベルヌイ数 / 代数曲線の一般射影及びchow形式 / 不分岐巡回拡大 / 一般相互法則 / ガロアの逆問題 / タイヒムーラー基本亜群 / チャウ形式 / 相互法則 / タイムヒーラー基本亜群 / fundamental unit / class number / power basis / unramified cyclic extension / Teichmuller groupoid / explicit reciprocity law / algebraic-geometric code / minimum distance / 整数還の巾底 / ネロン・テイト高さ / 類群及び単数群の構造 / Yokoi-Chowla予想 / 3次体 / Mordell Curves / 代数曲線 / タイヒミューラー基本亜群 / 基本単数系と類数 / p進表現 / Power Intetral basis / Fundamental Unit / Teichmueller grounoid / Neron-Tate Height / Elliptic Curve / Algebraic Geometry Code / アーベル拡大の整数環 / フェアリンデの公式 / Galois表現 / ポリアーベル拡大の整数環 / RSA署名 / 連立ベル方程式 / チャウ多様体 / Buchsbaum Stanley-Reisner ring / The ring of an abelian extension / Integral power basis / Class number / Elliptic curve / Verlinde's formula / 特殊線形群 / 整数基 / p-1次巡回拡大 / Siegel 保型形式 / ハッセの問題 / 不定方程式 / 超幾何微分方程式 / 保型形式のフーリエ係数 / LDPC符号 / 超グラフ / Integral basis / Cyclic extension of degree p-1 / Modular forms / Trace-norm code / Stanley-Reisner ring … More
Except Principal Investigator
リーマン面 / 代数曲線 / モジュライ空間 / タイヒミュラー基本亜群 / 代数幾何符号 / モノドロミー表現 / 保型形式 / ショットキー群 / Moduli space / ガロア表現 / 極小自由分解 / 超幾何微分方程式 / Stanley-Reisner環 / 正値解 / 全域解 / 減衰解 / 漸近挙動 / p進解析 / テ-タ関数 / ソリトン方程式 / エルミート符号 / 円分体 / 円単数 / 類数 / ガロア作用 / 一意化 / Algebraic curve / Teichmueller groupoid / Riemann surface / Monodromy representation / 共形場理論 / ボゴモロフ予想 / アーベル多様体 / ネロン・テイト高さ関数 / 超幾何方程式 / 整数環の巾底 / Cohen-Macaulay環 / 線形自由分解 / 重複度 / 正則度 / Stanley-Reisner ring / minimal free resolution / multiplicity / Siegel保型形式 / Stanley-Reisner 環 / 惰円型方程式系 / 準線形方程式系 / Supersolution-subsolution法 / Singular semilinear / チャウ形式 / 生成射影 / d重埋め込み / プリュッカー座標 / タイヒミュラー空間 / Feng-Raoの設定最小距離 / 単項式列 / 線形符号の復号法 / 2進L関数 / 合同関係式 / ヤコビの和 / ガウスの和 / ベルヌイ数 / 合同式 / 2次体 / イデアル類群 / 単数群 / 素因数分解アルゴリズム / 楕円曲線 / ヤコビ和 / RSA暗号 / Cyclotomic Field / Class Number / Congruence Relation / Quadratic Field / Ideal Class Group / Unit Group / Factorizing Algorithm / Elliptic Curve / 周期積分 / テータ関数 / フュージング・ムーヴ / Period integral / Theta function / Soliton equation / Automophic form / Galois action / 写像類群 / チャーン・サイモンズ積分 / Uniformization / Galois representation / Mapping class group / 超幾何学方程式 / アラケロフ幾何 / Conformal field theory / Teichmueller groupoids / Bogomolov conjecture / Abelian varieties / Neron-Tate height functions / hypergeometric equations / Riemann surfaces / 代数関数体 / 符号の最小距離 / 整数還の基本単数 / チャウ多様体 / グラースマン多様体 / 1次自由分解 / Hasseの単数指数 / Stanley-Reisner ideal / Algebraic Function Fields / Algebraic Geometry Codes / Minimum Distance of Codes / Fundamental Units / Teichmueller Groupoids / Monodromy Representation / Chow Varieties / Minimal Free Resolution / 代数曲線とリーマン面 / ALGEBRAIC CURVE / MODULI SPACE / GALOIS REPRESENTATION / CONFORMAL FIELD THEORY / MONODROMY REPRESENTATION / ABELIAN VARIETY / NERON-TATE'S HEIGHT / HYPERGEOMETRIC EQUATION / Stnaley-Reisner環 / Buchsbaum環 / Castelnuovo-Mumford正則度 / Buchsbaum / Cohen-Macaulay / Buchsbaum ring / Cohen-Macaulay ring / linear resolution / Castelnuovo-Mumford regularity / 誤り訂正符号 / 符号の代数的構成 / 低密度パリティ検査行列 / 整数環のべき基底 / 低密度パリティ検査 / Siegel 保型形式 / 最小距離 / LDPC符号 / 被約単項式イデアル / Error-correcting codes / Algebraic geometry codes / Algebraic cnnstruntion of codes / Low density parity check codes / Power bases of integer rings / Siegel modular forms / Stanley-Reisner rings / Riemann面 / Schottky群 / ベクトル束 / Abel-Jacobiの定理 / Verlindeの公式 / p進Siegel保型形式 / モノドロミー群 / フェアリンデ公式 / モジュライ / Schottky group / Vector bundle / Abel-Jacobi's theorem / Verlinde's formula / Siegel modular form / p-adic Siegel modular form / Castelnuovo-Mumford reaularity / 準線形楕円型偏微分方程式 / 劣線形方程式 / 外部境界値問題 / 極大正値減衰解 / 優関数ー劣関数法 / 最大値原理 / 準線形楕円型方程式 / 初期・境界値問題 / 優関数・劣関数法 / 極大解 / 非線形固有値問題 / supersolution-subsolution法 / Quasilinear elliptic equation / Sublinear equation / Exterior boundary value problem / Entire solution / Positive solution / Maximal solution / Supersolution-subsolution method Less
  • Research Projects

    (23 results)
  • Research Products

    (71 results)
  • Co-Researchers

    (33 People)
  •  Number Theory and its Development to Discrete MathematicsPrincipal Investigator

    • Principal Investigator
      NAKAHARA Toru
    • Project Period (FY)
      2008 – 2010
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Algebra
    • Research Institution
      Saga University
  •  Explicit construction of algebraic geometry codes

    • Principal Investigator
      UEHARA Tsuyoshi
    • Project Period (FY)
      2006 – 2007
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Algebra
    • Research Institution
      Saga University
  •  New construction of vector bundles on Riemann surfaces and Verlinde's formula

    • Principal Investigator
      ICHIKAWA Takashi
    • Project Period (FY)
      2006 – 2007
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Algebra
    • Research Institution
      Saga University
  •  Number Theory, Its Application to Discrete Mathematics and DevelopmentPrincipal Investigator

    • Principal Investigator
      NAKAHARA Toru
    • Project Period (FY)
      2006 – 2007
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Algebra
    • Research Institution
      Saga University
  •  Study on minimal free resolution of Stanley-Reisner rings

    • Principal Investigator
      TERAI Naoki
    • Project Period (FY)
      2006 – 2007
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Algebra
    • Research Institution
      Saga University
  •  Study on minimal free resolution of Stanley-Reisner rings

    • Principal Investigator
      TERAI Naoki
    • Project Period (FY)
      2004 – 2005
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Algebra
    • Research Institution
      Saga University
  •  Number Theory and Its Applications to Discrete MathematicsPrincipal Investigator

    • Principal Investigator
      NAKAHARA Toru
    • Project Period (FY)
      2004 – 2005
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Algebra
    • Research Institution
      Saga University
  •  VERTEX OPERATOR ALGEBRAS AND MODULI SPACES OF ALGEBRAIC CURVES

    • Principal Investigator
      ICHIKAWA Takashi
    • Project Period (FY)
      2003 – 2004
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Algebra
    • Research Institution
      SAGA UNIVERSITY
  •  Number Theory and Applications to the Related Discrete MathematicsPrincipal Investigator

    • Principal Investigator
      NAKAHARA Toru
    • Project Period (FY)
      2002 – 2003
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Algebra
    • Research Institution
      Saga University
  •  Minimum distance of error-correcting codes constructed by algebraic function fields

    • Principal Investigator
      UEHARA Tsuyoshi
    • Project Period (FY)
      2002 – 2003
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      General mathematics (including Probability theory/Statistical mathematics)
    • Research Institution
      Saga University
  •  Teichmueller groupoids and monodromy in conformal field theory

    • Principal Investigator
      ICHIKAWA Takashi
    • Project Period (FY)
      2001 – 2002
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Algebra
    • Research Institution
      Saga University
  •  Motivic aspect of moduli space of algebraic curves

    • Principal Investigator
      ICHIKAWA Takashi
    • Project Period (FY)
      1999 – 2000
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Algebra
    • Research Institution
      Saga University
  •  Number Theory and Its Apprication to Discrete MathematicsPrincipal Investigator

    • Principal Investigator
      NAKAHARA Toru
    • Project Period (FY)
      1999 – 2000
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Algebra
    • Research Institution
      Saga University
  •  Moduli space of algebraic curves and automorphic forms

    • Principal Investigator
      ICHIKAWA Takashi
    • Project Period (FY)
      1997 – 1998
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Algebra
    • Research Institution
      Saga University
  •  代数曲線から生成される誤り訂正符号の研究

    • Principal Investigator
      上原 健
    • Project Period (FY)
      1996
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Algebra
    • Research Institution
      Saga University
  •  無限種数解析曲線とソリトン方程式

    • Principal Investigator
      市川 尚志
    • Project Period (FY)
      1995
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      Algebra
    • Research Institution
      Saga University
  •  代数多様体のモヂュライ理論の研究

    • Principal Investigator
      TANAKA Tatsuji
    • Project Period (FY)
      1993
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      Algebra
    • Research Institution
      Saga University
  •  整数論及びその学際領域の研究Principal Investigator

    • Principal Investigator
      中原 徹
    • Project Period (FY)
      1993
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      Algebra
    • Research Institution
      Saga University
  •  非線形楕円型偏微分方程式

    • Principal Investigator
      FURUSHO Yasuhiro
    • Project Period (FY)
      1992
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      解析学
    • Research Institution
      Saga University
  •  Congruence relations between class numbers of cyclotomic fields

    • Principal Investigator
      UEHARA Tsuyoshi
    • Project Period (FY)
      1990 – 1991
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      代数学・幾何学
    • Research Institution
      Saga University
  •  整数論Principal Investigator

    • Principal Investigator
      中原 徹
    • Project Period (FY)
      1988 – 1989
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      代数学・幾何学
    • Research Institution
      Saga University
  •  Study of Nonlinear Partial Differential Equations of Elliptic Type

    • Principal Investigator
      FURUSHO Yasuhiro
    • Project Period (FY)
      1987 – 1988
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      解析学
    • Research Institution
      Saga University
  •  円単数およびヤコビの和の研究

    • Principal Investigator
      上原 健
    • Project Period (FY)
      1986
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      代数学・幾何学
    • Research Institution
      Saga University

All 2011 2010 2009 2008 2007 2006 2005 2004 Other

All Journal Article Presentation Book

  • [Book] 線形代数入門[国内大学生協より頒布]2010

    • Author(s)
      中原徹, 片山眞一, 小林孝行, 工藤愛知
    • Publisher
      学術図書出版社
    • Data Source
      KAKENHI-PROJECT-20540019
  • [Book] 線形代数入門[大学生協より頒布,市販版は2011年秋に出版予定]2010

    • Author(s)
      中原徹, 片山眞一, 小林孝行, 工藤愛知
    • Publisher
      学術図書出版社
    • Data Source
      KAKENHI-PROJECT-20540019
  • [Book] 線形代数入門ISBN978-4-7806-0104-62009

    • Author(s)
      中原徹, 片山 眞一, 小林孝行, 工藤愛知
    • Publisher
      学術図書出版社
    • Data Source
      KAKENHI-PROJECT-20540019
  • [Book] 線形代数入門2009

    • Author(s)
      中原徹, 片山眞一, 小林孝行, 工藤愛知
    • Publisher
      学術図書出版社
    • Data Source
      KAKENHI-PROJECT-20540019
  • [Book] Introduction to Linear Algebra2008

    • Author(s)
      T., Nakahara, S. I. A., Shah
    • Total Pages
      167
    • Publisher
      Gakujyutsu Tosho Shuppansha
    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-18540040
  • [Book] 線形代数入門 (各大学内頒布版)2008

    • Author(s)
      中原 徹, 片山 真一, 小林 孝行, 工藤 愛知
    • Total Pages
      167
    • Publisher
      学術図書出版社
    • Data Source
      KAKENHI-PROJECT-18540040
  • [Book] 線形代数入門(国内大学頒布版)2008

    • Author(s)
      中原 徹, 片山 真一, 小林 孝行, 工藤 愛知
    • Total Pages
      167
    • Publisher
      学術図書出版社
    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-18540040
  • [Book] Proceedings of the 2003 Nagoya Conference Yokoi-Chowla Conjecture and Related Problems2004

    • Author(s)
      [BKLN] S.Katayama, C.Levesque, T.Nakahara
    • Total Pages
      148
    • Publisher
      Furukawa Total Printing Co. LTD, Saga Japan, ix + 139 (March 2004, November 2004(revised edition)),
    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-16540029
  • [Book] Proceedings of the 2003 Nagoya Conference Yokoi-Chowla Conjecture and Related Problems2004

    • Author(s)
      [BKLN]S.Katayama, C.Levesque, T.Nakahara
    • Publisher
      Furukawa Total Printing Co.LTD, Saga Japan (March 2004, November 2004(revised edition))
    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-16540029
  • [Book] Proceedings of the 2003 Nagoya Conference Yokoi-Chowla Conjecture and Related Problems2004

    • Author(s)
      S.Katayama, C.Levesque, T.Nakahara
    • Total Pages
      139
    • Publisher
      Furukawa Total Printing Co.LTD
    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-15540036
  • [Book] Proceedings of the 2003 Nagoya Conference Yokoi-Chowla Conjecture and Related Problems2004

    • Author(s)
      Shnichi Katayama, Claude Levesque, Toru Nakahara
    • Total Pages
      139
    • Publisher
      Furukawa Total Printing Co. LTD
    • Data Source
      KAKENHI-PROJECT-15540036
  • [Book] [BKLN] Proceedings of the 2003 Nagoya Conference Yokoi-Chowla Conjecture and Related Problems(revised edition)2004

    • Author(s)
      S.-I.Katayama, C.Levesque, T.Nakahara
    • Total Pages
      148
    • Publisher
      Furukawa Total Printing Co. LTD, Saga Japan, ix + 139 (March 2004, November 2004),
    • Data Source
      KAKENHI-PROJECT-16540029
  • [Book] Proceedings of the 2003 Nagoya Conference, Yokoi-Chowla Conjecture and Related Problems2004

    • Author(s)
      Shinnichi Katayama, Claude Levesque, Toru Nakahara
    • Total Pages
      139
    • Publisher
      Furukawa Total Printing Co.LTD
    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-15540036
  • [Journal Article] Hasse's Problem for monogenic fields2009

    • Author(s)
      T.Nakahara
    • Journal Title

      Annales Mathema -tiques Blaise Pascal 16

      Pages: 47-56

    • Data Source
      KAKENHI-PROJECT-20540019
  • [Journal Article] On a problem of Hasse2009

    • Author(s)
      Y.Motoda, T.Nakahara, S.I.AShah, T.Uehara
    • Journal Title

      RIMS Kokyuroku Bessatsu B12

      Pages: 209-221

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20540019
  • [Journal Article] On a Problem of Hasse2009

    • Author(s)
      Yasuo Motoda, Toru Nakahara, S. I. A. Shah, Tsuyoshi Uehara
    • Journal Title

      RIMS Kokyuroku Bessatsu, Res. Inst. Math. Sci. (RIMS), Kyoto Univ. (To appear)

      Pages: 13-13

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20540019
  • [Journal Article] Orbit of quadratic irrationals modulo $p$ by the modular group2009

    • Author(s)
      T.Nakahara, S.-i.Katayama, S.I.A.Shah, M.N.Khalid, S.Badshah
    • Journal Title

      Journal of Research Gomal University 25

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20540019
  • [Journal Article] Orbit of quadratic irrationals modulo $p$ by the modular group2009

    • Author(s)
      S.-i.Katayama, T.Nakahara, S.I.A.Shah, Mohammad Naeem Khalid, Sareer Badshah
    • Journal Title

      Journal of Research Gomal University 25

      Pages: 1-5

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20540019
  • [Journal Article] On a problem of Hasse2009

    • Author(s)
      Y.Motoda, T.Nakahara, S.I.A.Shah, T.Uehara
    • Journal Title

      RIMS Kokyuroku Bessatsu B12

      Pages: 209-221

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20540019
  • [Journal Article] Hasse's problem for monogenic fields2009

    • Author(s)
      Toru Nakahara
    • Journal Title

      Annales math\' ematiques Blaise Pascal 16-1

      Pages: 47-56

    • Data Source
      KAKENHI-PROJECT-20540019
  • [Journal Article] On integral bases of the octic 2-elementary abelian extension fields2008

    • Author(s)
      Kyoung Ho Park, Toru Nakahara, Yasuo Motoda
    • Journal Title

      Kyushu J. of Mathematics ([LaTeX])

      Pages: 12-12

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-18540040
  • [Journal Article] On power integral bases of the 2-elementary abelian extension fields2006

    • Author(s)
      Yasuo, Motoda, Toru, Nakahara, Kyoung Ho, Park
    • Journal Title

      Trends in Mathematics 9-1

      Pages: 55-63

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-18540038
  • [Journal Article] On power integral bases of the 2-elementary abelian extension fields2006

    • Author(s)
      [MNP] Y.Motoda, T.Nakahara, K.-H.Park
    • Journal Title

      Proceedings "Trends in Mathematics" of Korea-Japan joint seminar in KAIST 2006 To appear

      Pages: 9-9

    • Data Source
      KAKENHI-PROJECT-16540029
  • [Journal Article] On power integral bases of the 2-elementary abelian extension fields2006

    • Author(s)
      Y.Motoda, T.Nakahara, K.H.Park
    • Journal Title

      Trends in Mathematics 9・1

      Pages: 55-63

    • Data Source
      KAKENHI-PROJECT-18540040
  • [Journal Article] On power integral bases of the 2-elementary abelian extension fields2006

    • Author(s)
      [MNP] Y.Motoda, T.Nakahara, K.-H.Park
    • Journal Title

      Proceedings "Trends in Mathematics" of Korea-Japan joint seminar in KAIST 2006 (To appear)

    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-16540029
  • [Journal Article] On power integral bases of the 2-elementary abelian extension field2006

    • Author(s)
      [MNP]Y.Motoda, T.Nakahara, K.-H.Park
    • Journal Title

      Proceedings "Trends in Mathematics" of Korea-Japan joint seminar in KAIST 2006, (To appear)

      Pages: 9-9

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-16540029
  • [Journal Article] On integral bases of real octic 2-elementary abelian extensions2006

    • Author(s)
      K.H.Park, T.Nakahara, Y.Motoda
    • Journal Title

      京都大学数理解析研究所講究録「代数的整数論とその周辺」 1521

      Pages: 176-184

    • Data Source
      KAKENHI-PROJECT-18540040
  • [Journal Article] On-Integral Bases of Certain Real Octic Abelian Field2005

    • Author(s)
      [PMN]K.-H.Park, Y.Motoda, T.Nakahara
    • Journal Title

      Rep.Sci.Engrg.Saga Univ.Math. 34・1

      Pages: 1-15

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-16540029
  • [Journal Article] On Integral Bases of Certain Real Octic Abelian Field2005

    • Author(s)
      [PMN] K.-H.Park, Y.Motoda, T.Nakahara
    • Journal Title

      Rep.Sci.Engrg.Saga Univ.Math. 34・1

      Pages: 1-15

    • Data Source
      KAKENHI-PROJECT-16540029
  • [Journal Article] On Integral Bases of Certain Real Octic Abelian Field2005

    • Author(s)
      [PMN] K.-H.Park, Y.Motoda, T.Nakahara
    • Journal Title

      Rep. Sci. Engrg. Saga Univ. Math. 34・1

      Pages: 1-15

    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-16540029
  • [Journal Article] Recent progress of Hasse's problem on power integral bases of abelian fields,2004

    • Author(s)
      [NSU]T.Nakahara, S.I.A.Shah, T.Uehara
    • Journal Title

      Proceedings of the Japan-Korea Joint Seminar on Number Theory (Edited by H.K.Kim, Y.Taguchi)

      Pages: 131-136

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-16540029
  • [Journal Article] [MN1] Monogenesis of Algebraic Number Fields whose Galois Groups are 2-elementary Abelian2004

    • Author(s)
      Y.Motoda, T.Nakahara
    • Journal Title

      Proceedings of the Nagoya Conference Yokoi-Chowla Conjecture and Related Problems Edited by S.Katayama

      Pages: 91-99

    • Data Source
      KAKENHI-PROJECT-16540029
  • [Journal Article] On a family of real bicyclic biquadratic fields2004

    • Author(s)
      [KLN]S.Katayama, C.Levesque, T.Nakahara
    • Journal Title

      Centre de Recherches Mathematiques CRW Proceedings and Lecture Notes 36

      Pages: 177-188

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-16540029
  • [Journal Article] Power integral bases in algebraic number fields whose Galois groups are 2-elementary abelian2004

    • Author(s)
      Yasuo Motoda, Toru Nakahara
    • Journal Title

      Arch.Math. 83

      Pages: 309-316

    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-15540036
  • [Journal Article] [NSU] Recent progress of Hasse's problem on power integral bases of abelian fields,2004

    • Author(s)
      T.Nakahara, S.I.A.Shah, T.Uehara
    • Journal Title

      Proceedings of the Japan-Korea Joint Seminar on Number Theory (Edited by H.K.Kim and Y.Taguchi)

      Pages: 131-136

    • Data Source
      KAKENHI-PROJECT-16540029
  • [Journal Article] Monogenesis of Algebraic Number Fields whose Galois Groups are 2-elementary Abelian2004

    • Author(s)
      [MN] Y.Motoda, T.Nakahara
    • Journal Title

      Arch. Math 83

      Pages: 309-316

    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-16540029
  • [Journal Article] Recent progress of Hasse's problem on power integral bases of abelian fields,2004

    • Author(s)
      [NSU] T.Nakahara, S.I.A.Shah, T.Uehara
    • Journal Title

      Proceedings of the Japan-Korea Joint Seminar on Number Theory(Edited by H. K. Kim, Y. Taguchi)

      Pages: 131-136

    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-16540029
  • [Journal Article] Recent Progress of Hasse's Problem on power integral bases of abelian fields2004

    • Author(s)
      中原徹, 上原健 他
    • Journal Title

      Proceedings of Japan-Korea joint seminar on Number Theory

      Pages: 131-136

    • Data Source
      KAKENHI-PROJECT-16540028
  • [Journal Article] [MN2] Power integral bases in algebraic number fields whose galois groups are 2-elementary abelian,2004

    • Author(s)
      Y.Motoda, T.Nakahara
    • Journal Title

      Arch.Math 83

      Pages: 309-316

    • Data Source
      KAKENHI-PROJECT-16540029
  • [Journal Article] On a family of real bicyclic biquadratic fields2004

    • Author(s)
      [KLN] S.Katayama, C.Levesque, T.Nakahara
    • Journal Title

      Centre de Recherches Mathematiques CRW Proceedings and Lecture Notes 36

      Pages: 177-188

    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-16540029
  • [Journal Article] Monogenesis of Algebraic Number Fields whose Galois Groups are 2-elementary Abelian2004

    • Author(s)
      [MN]Y.Motoda, T.Nakahara
    • Journal Title

      Arch.Math 83

      Pages: 309-316

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-16540029
  • [Journal Article] [KLN] On a family of real bicyclic biquadratic fields2004

    • Author(s)
      S.-I.Katayama, C.Levesque, T.Nakahara
    • Journal Title

      Centre de Recherches Mathematiques CRW Proceedings and Lecture Notes 36

      Pages: 177-187

    • Data Source
      KAKENHI-PROJECT-16540029
  • [Journal Article] Hasse's problem for monogenic fields

    • Author(s)
      Toru Nakahara
    • Journal Title

      Proc. of International Conference ''Algebra, Number Theory and their applications'' Oujda-Saidia Morocco, 2006 (to appear)

    • Data Source
      KAKENHI-PROJECT-18540038
  • [Journal Article] On integral bases of the octic 2-elementary abelian extension fields

    • Author(s)
      Kyoung, Ho, Park, Toru, Nakahara, Yasuo, Motoda
    • Journal Title

      Kyushu J. of Mathematics (to be revised)

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-18540040
  • [Journal Article] Hasse's problem for monogenic fields

    • Author(s)
      T.Nakahara
    • Journal Title

      Proc. of International Conference'' Algebra, Number Theory and their applications'' Oujda-Saidia Morocco, 2006 (To appear)

      Pages: 8-8

    • Data Source
      KAKENHI-PROJECT-18540040
  • [Journal Article] On integral bases of the octic 2-elementary abelian extension fields

    • Author(s)
      K.-H.Park, T.Nakahara, Y.Motoda
    • Journal Title

      Kyushu Journal of Mathematics (to apper)

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-18540038
  • [Presentation] On certain pure octic fields related to a Problem of Hasse2011

    • Author(s)
      中原徹
    • Organizer
      Workshop on Number Theory in Saga 2011 Winter
    • Place of Presentation
      佐賀大学
    • Year and Date
      2011-01-09
    • Data Source
      KAKENHI-PROJECT-20540019
  • [Presentation] ハッセの問題に関連する或る純8次体について2011

    • Author(s)
      アブドゥルハミード, 中原徹, シャーザッドアハマッド, サイエッドハスネーヌ
    • Organizer
      Workshop on Number Theory in Saga 2011 Winter
    • Place of Presentation
      佐賀大学
    • Year and Date
      2011-01-09
    • Data Source
      KAKENHI-PROJECT-20540019
  • [Presentation] On Monogeneity of Certain Pure Sextic Number Fields2010

    • Author(s)
      Toru Nakahara
    • Organizer
      Workshop on Number Theory in Saga 2010 Summer
    • Place of Presentation
      佐賀大学
    • Year and Date
      2010-08-13
    • Data Source
      KAKENHI-PROJECT-20540019
  • [Presentation] Gauss sum and its application to a proof of the reciprocity law of quadratic residues2010

    • Author(s)
      T.Nakahara
    • Organizer
      1st Peshawar Research Seminar(招待講演)
    • Place of Presentation
      NUCES, Peshawar Campus, Pakistan
    • Year and Date
      2010-02-12
    • Data Source
      KAKENHI-PROJECT-20540019
  • [Presentation] Gauss sum and Jacobi sum attached to the sextic character of prime conductor2010

    • Author(s)
      T.Nakahara
    • Organizer
      Workshop in Number Theory in Saga 2010
    • Place of Presentation
      Saga Univ., Japan
    • Year and Date
      2010-01-12
    • Data Source
      KAKENHI-PROJECT-20540019
  • [Presentation] On Monogeneity of Certain Pure Sextic Number Fields2010

    • Author(s)
      S.Ahmad, T.Nakahara, S.Husnine, A.Hameed
    • Organizer
      Workshop on Number Theory in Saga 2010 Summer
    • Place of Presentation
      Saga University
    • Year and Date
      2010-08-13
    • Data Source
      KAKENHI-PROJECT-20540019
  • [Presentation] Gauss sum and Jacobi sum attached to the sextic character of prime conductor2010

    • Author(s)
      中原徹
    • Organizer
      Workshop on Number Theory in Saga 2010
    • Place of Presentation
      Saga University
    • Year and Date
      2010-01-12
    • Data Source
      KAKENHI-PROJECT-20540019
  • [Presentation] Classification of monogenic cyclic quartic fields of even conductor2009

    • Author(s)
      Toru Nakahara
    • Organizer
      Workshop on Number Theory in Saga 2009
    • Place of Presentation
      佐賀大学
    • Year and Date
      2009-01-05
    • Data Source
      KAKENHI-PROJECT-20540019
  • [Presentation] Monogenic cyclic sextic fields of prime conductor and gauss sum2009

    • Author(s)
      中原徹
    • Organizer
      Workshop on Number Theory in Saga 2009 Summer
    • Place of Presentation
      Saga University
    • Year and Date
      2009-08-04
    • Data Source
      KAKENHI-PROJECT-20540019
  • [Presentation] Classification of monogenic cyclic quartic fields of even conductor2009

    • Author(s)
      中原徹
    • Organizer
      Workshop on Number Theory in Saga 2009
    • Place of Presentation
      Saga University
    • Year and Date
      2009-01-05
    • Data Source
      KAKENHI-PROJECT-20540019
  • [Presentation] Monogenic cyclic sextic fields of prime conductor and Gauss sum2009

    • Author(s)
      T.Nakahara
    • Organizer
      Workshop in Number Theory in Saga 2009
    • Place of Presentation
      Saga Univ., Japan
    • Year and Date
      2009-08-04
    • Data Source
      KAKENHI-PROJECT-20540019
  • [Presentation] Hasse's problem for Integral Power Bases of Abelian Number Fields [招待講演]2009

    • Author(s)
      Toru Nakahara
    • Organizer
      Special Seminar, Quaid-i-Azam Univ.
    • Place of Presentation
      Islamabad, the Islami Republic of Pakistan
    • Year and Date
      2009-03-26
    • Data Source
      KAKENHI-PROJECT-20540019
  • [Presentation] On a problem of Hasse for cyclic quartic fields[招待講演]2008

    • Author(s)
      Toru Nakahara
    • Organizer
      Algebra and Number Theory Seminar, National Univ. of Science and Technology
    • Place of Presentation
      Islamabad, the Islami Republic of Pakistan
    • Year and Date
      2008-11-12
    • Data Source
      KAKENHI-PROJECT-20540019
  • [Presentation] Orbit of quadratic irrationals modulo p by the modular group2008

    • Author(s)
      Toru Nakahara
    • Organizer
      8th International Pure Mathematics Conference 2007[招待講演]
    • Place of Presentation
      パキスタン・イスラム共和国イスラマバード
    • Year and Date
      2008-08-24
    • Data Source
      KAKENHI-PROJECT-18540040
  • [Presentation] Introduction to a problem of Hasse for abelian number fields[招待講演]2008

    • Author(s)
      Toru Nakahara
    • Organizer
      Workshop/Seminar in Mathematics, National Univ. of Computer and Emerging Sciences[NUCES], Lahore Campus
    • Place of Presentation
      Lahore, the Islami Republicof Paki Stan
    • Data Source
      KAKENHI-PROJECT-20540019
  • [Presentation] A problem of Hasse and different2008

    • Author(s)
      T., Nakahara
    • Organizer
      Seminar on Algebra
    • Place of Presentation
      Kyushu Univ
    • Year and Date
      2008-02-22
    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-18540040
  • [Presentation] ハッセの問題と共役差積2008

    • Author(s)
      中原 徹
    • Organizer
      九州大学代数学セミナー[招待講演]
    • Place of Presentation
      九州大学理学部
    • Year and Date
      2008-02-22
    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-18540040
  • [Presentation] ハッセの問題と共役差2008

    • Author(s)
      中原 徹
    • Organizer
      九州大学代数学セミナー [招待講演]
    • Place of Presentation
      九州大学理学部
    • Year and Date
      2008-02-22
    • Data Source
      KAKENHI-PROJECT-18540040
  • [Presentation] Orbits of irrationals by the modular group in a real quadratic field2007

    • Author(s)
      Toru, Nakahara
    • Organizer
      The 17th International Conference of Jangjeon Mathematical Society
    • Place of Presentation
      Kyungpook National University the Republic of Korea
    • Year and Date
      2007-07-08
    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-18540038
  • [Presentation] Orbit of quadratic irrationals modulo p by the modular group2007

    • Author(s)
      Toru Nakahara, Syed, Inayat, Ali, Shah
    • Organizer
      8th International Pure Mathematics Conference 2007[招待講演]
    • Place of Presentation
      パキスタン・イスラム共和国イスラマバード
    • Year and Date
      2007-08-24
    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-18540040
  • [Presentation] On a Problem of Hasse2007

    • Author(s)
      S. I. A., Shah, Y., Motoda, T., Nakahara, T., Uehara
    • Organizer
      Algebraic Number Theory and its related Topics(RIMS Kyoto Univ.)
    • Place of Presentation
      Kyoto
    • Year and Date
      2007-12-13
    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-18540040
  • [Presentation] ハッセの問題について2007

    • Author(s)
      元田 康夫、中原 徹、上原 健、シャー・サイエッド・イナヤット・アリ
    • Organizer
      研究集会「代数的整数論とその周辺」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2007-12-13
    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-18540038
  • [Presentation] Orbit of quadratic irrationals modulo p by the modular group2007

    • Author(s)
      T., Nakahara, S. I. A., Shah
    • Organizer
      8th International Pure Mathematics Conference 2007
    • Place of Presentation
      Islamabad, the Islamic Republic of Pakistan
    • Year and Date
      2007-08-24
    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-18540040
  • [Presentation] On Hasse's Problem2007

    • Author(s)
      Y., Motoda, T., Nakahara, T., Uehara, S.I.A., Shah
    • Organizer
      Symposium on Algebraic Number Theory and its Related Area
    • Place of Presentation
      Kyoto Univ
    • Year and Date
      2007-12-13
    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-18540038
  • [Presentation] ハッセの問題について2007

    • Author(s)
      元田 康夫, 中原 徹, 上原 健, SHAH, Syed, Inayat, Ali
    • Organizer
      研究集会「代数的整数論とその周辺」[招待講演]
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2007-12-13
    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-18540040
  • 1.  UEHARA Tsuyoshi (80093970)
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  • 2.  ICHIKAWA Takashi (20201923)
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