AOKI Noboru 青木昇

… Alternative Names

Researcher Number	30183130
Other IDs
Affiliation (Current)	2019: 立教大学, 理学部, 教授
Affiliation (based on the past Project Information) *help	2016: 立教大学, 理学部, 教授 2003 – 2009: 立教大学, 理学部, 教授 1995 – 2002: 立教大学, 理学部, 助教授 1991 – 1994: DEPT. MATH., RIKKYO UNIV., LECTURER, 理学部, 講師 1988: 立教大学, 理学部, 助手
Review Section/Research Field	Principal Investigator Algebra / Algebra Except Principal Investigator Algebra / 代数学・幾何学 / Algebra
Keywords	Principal Investigator 楕円曲線 / アーベル多様体 / ヤコビ和 / L関数 / ガウス和 / Jacobi sum / Tate-Shafarevich group / イデアル類群 / Fermat curve / ゼータ関数 … More Except Principal Investigator モーデル・ヴェイユ格子 / 楕円曲面 / Mordell-Weil Lattices / テイト・シャファレヴィチ群 / 整数点 / モ-デル・ヴェイユ格子 / 代数曲線 / Maass wave forms / 概均質ベクトル空間 / 楕円曲線 / 特異ファイバー / 有理楕円曲面 / Fermat曲線 / 整点 / ハイト公式 / 相対跡公式 / 符号 / Selberg zeta関数 / 消滅ルート(vanishing root) / 球体充填 / ホッジ予想 / Shafarevich Correspondence / フェルマ曲線 / 極大有理連結ファイブレ-ション / 一般Hecke作用素 / ラングランズ対応 / 球の詰め込み問題 / Involutions / 対称多様体 / 多重L-値 / パンルヴェ方程式 / 概均質ゼータ関数 / KaGG"HHhlenーEinstein計量 / ネロン・セヴェリ格子 / 交点理論 / 曲面孤立特異点 / 楕円モデュラ-型式 / 楕円ファイブレーション / Hodge予想 / ネロン・セベリ群 / 超局所化 / 佐武図式 / シュバレー群 / 曲面上の曲線族 / クンマー曲面 / ネロン・セヴェリ群 / 保型形式 / ３次曲面と２７直線 / 代数幾何学 / 対合 / ピカール数 / 分類理論 / L関数の零点 / 種数 / Hecke作用素 / 線型代数群 / DS-トリプル / 射影空間・二次超曲面 / ホッジ・サイクル / zeta regularization / 有理連結性 / Shimura 対応 / Selberg跡公式 / ワイヤストラス変換 / Abelian Varieties / Fermat curves / アーペル多様体 / 相対双対層 / アフィン類似 / フェルマー曲面 / Hodge Conjecture / モーデル・ヴェイユ群 / Davenportの限界 / 不定符号4元数環 / アーベル多様体 / Jacobi形式 / 局所ゼータ関数 / Selberg zeta 関数 / MODELL-WEIL LATTICES / maximal rationally connected fibration / prime geodesic theorem / コレスポンデンス / Painleve equations / Selberg zeta functions / converse theorem / ガロア表現 / DSトリプル / 楕円パラメータ / DS-triples / Sphere packing problem / 一般型多様体 / 対称対 / コード / Jacobi forms / 乗法的卓越族 / relative deformation / Tate-Shafarevich group / b-function / Affineanalogues / JACOBIAN VARIETIES / 球のつめこみ / abc-定理 / K3 surfaces / 構成可能層 / ガウス和 / Linear Algelvaic Groups / 標数2の体上の代数群 / abc-theorem / モジュラー群 / ABC定理 / modular forms / Mordell-Weil格子 / INTERSECTION THEORY / Elliptic Surface / Q上の楕円曲線 / Kummer surfaces / 楕円曲線の優美族 / 3次曲面と２７直線 / 不変式論 / ゼータ関数 / Symmetric Pairs / Relative Trace Formake / ランク / Monoge-Ampere方程式 / b-関数 / 極大有理連結部分多様体 / Hodge Cycles / Fano manifolds / Maass波形式 / 球体充てん / 制限ルート系 / 相対変形 / ヤコビ多様体 / 反射層 / セルバーグゼータ関数 / 標数2の体 / UNITS / 高種数の代数曲線 / 超幾何関数 / Rational elliptic surfaces / prehomogeneous vector space / MordellーWeil格子 / Davenport-Stothers3対 / 高種数ファイブレーション / 簡約代数群 / curves on a surface / 単数 / Elliptic Modular Surfaces / Mardell-Weil lattices / Codes / 位相型の有限性 / Gamma行列 / Weierstrass部分空間 / 関数体 / 高種数曲線ファイブレーション / 極大有理連結ファイブレーション / L-関数 / 生成元 / K3曲面 / 代数群 / multiple L-values / サイクル / 素測地線定理 / sphere packing / 相対変形理論 / 楕円モジュラー曲面 / 分解体 / K３曲面 / Tate-Shafarevich Group / 極大な特異ファイバー / projective spaces and hyperquadrics / Integral Points / モデユライ理論 / Gauss sums / SPLITTING FIELDS / 多重L値 / Fano多様体 / double shuffle relation / ソリトン方程式 / 有界性定理 / シャファレヴィチ対応 / Singular fibre / Elliptic Curves / 弱球等質空間 Less

Studies of Mordell-Weil Lattices
- Principal Investigator
  
  SHIODA Tetsuji
- Project Period (FY)
  2013 – 2016
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Rikkyo University
Studies on arithmetic problems on abelian varietiesPrincipal Investigator
- Principal Investigator
  
  AOKI Noboru
- Project Period (FY)
  2006 – 2009
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Rikkyo University
Mordell-Weil Lattices and Cycles on Algebraic Surfaces
- Principal Investigator
  
  SHIODA Tetsuji
- Project Period (FY)
  2005 – 2007
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Rikkyo University
Shafarevich Correspondence and Mordell-Weil Lattices
- Principal Investigator
  
  SHIODA Tetsuji
- Project Period (FY)
  2003 – 2004
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  RIKKYO UNIVERSITY
Study on interrelations among quadratic forms, automorphic forms and related various zeta-functionsPrincipal Investigator
- Principal Investigator
  
  AOKI Noboru
- Project Period (FY)
  2003 – 2005
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Rikkyo University
Mordell-Weil Lattices of Elliptic Curves and Abelian Varieties
- Principal Investigator
  
  SHIODA Tetsuji
- Project Period (FY)
  2000 – 2002
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  RIKKYO UNIVERSITY
Study of zeta functions related to Jacobi forms and Siegel modular forms
- Principal Investigator
  
  ARAKAWA Tsuneo
- Project Period (FY)
  2000 – 2002
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  RIKKYO UNIVERSITY
SYMMETRIC PAIRS
- Principal Investigator
  
  UZAWA Tooru
- Project Period (FY)
  1998 – 2000
- Research Category
  
  Grant-in-Aid for Scientific Research (B).
- Research Field
  
  Algebra
- Research Institution
  RIKKYO UNIVERSITY
MORDELL-WEIL LATTICES OF JACOBIAN VARIETIES
- Principal Investigator
  
  SHIODA Tetsuji
- Project Period (FY)
  1997 – 1999
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  RIKKYO UNIVERSITY
Rational points on algebraic curves and its application to number theoryPrincipal Investigator
- Principal Investigator
  
  AOKI Noboru
- Project Period (FY)
  1997 – 1998
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  RIKKYO UNIVERSITY
モ-デル・ヴェイユ格子の理論と種々の応用
- Principal Investigator
  
  塩田徹治
- Project Period (FY)
  1996
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Rikkyo University
アーベル多様体の算術的理論の研究Principal Investigator
- Principal Investigator
  
  青木昇
- Project Period (FY)
  1995
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Rikkyo University
楕円曲線の算術的理論の研究Principal Investigator
- Principal Investigator
  
  青木昇
- Project Period (FY)
  1994
- Research Category
  
  Grant-in-Aid for Encouragement of Young Scientists (A)
- Research Field
  
  Algebra
- Research Institution
  Rikkyo University
L関の特殊値の研究Principal Investigator
- Principal Investigator
  
  青木昇
- Project Period (FY)
  1993
- Research Category
  
  Grant-in-Aid for Encouragement of Young Scientists (A)
- Research Field
  
  Algebra
- Research Institution
  Rikkyo University
モーデルヴェイユ格子の研究
- Principal Investigator
  
  SHIODA Tetuji
- Project Period (FY)
  1992
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  代数学・幾何学
- Research Institution
  Rikkyo University
THEORY OF ALGEBRAIC VARIETIES AND APPLICATIONS TO RELATED TOPICS
- Principal Investigator
  
  MIYAOKA Yoichi
- Project Period (FY)
  1989 – 1991
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  代数学・幾何学
- Research Institution
  RIKKYO UNIVERSITY
  Tokyo Metropolitan University
数論的幾何と代数的サイクルの研究
- Principal Investigator
  
  塩田徹治
- Project Period (FY)
  1988
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  代数学・幾何学
- Research Institution
  Rikkyo University

All 2010 2008 2007 2006 2005 2004 2003

All Journal Article

[Journal Article] Correction and supplement to the paper "Generators of the Neron-Severi group of a Fermat surface"2010
- Author(s)
  N. Aoki, T. Shioda
- Journal Title
  
  Comment. Math. Univ. Sancti Pauli 59巻
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540055
[Journal Article] On supersingular cyclic quotients of Fermat curves2008
- Author(s)
  N. Aoki
- Journal Title
  
  Comment. Math. Univ. Sancti Pauli 57巻
  
  Pages: 65-90
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540055
[Journal Article] On supersingular cyclic quotients of Fermat curves2008
- Author(s)
  Noboru Aoki
- Journal Title
  
  Commentarii Mathematici Universitatis Sancti Pauli 57
  
  Pages: 65-90
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540055
[Journal Article] On the zeta function of some cyclic quotients of Fermat curves2008
- Author(s)
  N. Aoki
- Journal Title
  
  Comment. Math. Univ. Sancti Pauli 57巻
  
  Pages: 163-185
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540055
[Journal Article] On the zeta function of some cyclic quotients of Fermat curves2008
- Author(s)
  Noboru Aoki
- Journal Title
  
  Commentarii Mathematici Universitatis Sancti Pauli 57巻
  
  Pages: 163-185
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540055
[Journal Article] On the zeta funcion of some cyclic quotients of Fermat curves2008
- Author(s)
  Noboru Aoki
- Journal Title
  
  Commentarii Mathematici Universitatis Sancti Pauli 57
  
  Pages: 163-185
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540055
[Journal Article] On supersingular cyclic quotients of Fermat curves2008
- Author(s)
  Noboru Aoki
- Journal Title
  
  Commentarii Mathematici Universitatis Sancti Pauli 57巻
  
  Pages: 65-90
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540055
[Journal Article] [10]On the solvebility of a certain linear Diophantine equation with a parity condition2007
- Author(s)
  Noboru Aoki
- Journal Title
  
  Comment.Math.Univ.St.Pauli 56
  
  Pages: 71-96
- Description
  「研究成果報告書概要(和文)」より
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-17540044
[Journal Article] On the solvability of a certain Diophantine equation with a parity condition2007
- Author(s)
  Noboru Aoki
- Journal Title
  
  Commentarii Mathematici Universitatis Sancti Pauli 56巻
  
  Pages: 71-96
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540055
[Journal Article] On the Solvability of a Certain Diophantine Equation with a Parity Condition2007
- Author(s)
  Noboru Aoki
- Journal Title
  
  Commentarii Mathematici Universitatis Sancti Pauli 56
  
  Pages: 71-96
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540055
[Journal Article] On the solvebility of a certain linear Diophantine equation with a parity condition2007
- Author(s)
  Noboru Aoki
- Journal Title
  
  Comment. Math. Univ. St. Pauli 56
  
  Pages: 71-96
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-17540044
[Journal Article] On the solvability of a certain linear Diophantine equation with a parity condition2007
- Author(s)
  N. Aoki
- Journal Title
  
  Comment. Math. Univ. Sancti Pauli 56巻
  
  Pages: 71-96
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540055
[Journal Article] Torsion points on CM abelian varieties2006
- Author(s)
  Noboru Aoki
- Journal Title
  
  Commentarii Mathematici Universitatis Sancti Pauli 55巻
  
  Pages: 207-229
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540055
[Journal Article] Survey of Gross's conjecture and its refinements2006
- Author(s)
  N. Aoki, J. Lee
- Journal Title
  
  9巻
  
  Pages: 31-34
- Data Source
  KAKENHI-PROJECT-18540055
[Journal Article] Torsion points on CM abelian varieties2006
- Author(s)
  N. Aoki
- Journal Title
  
  Comment. Math. Univ. Sancti Pauli 55巻
  
  Pages: 207-229
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540055
[Journal Article] Torsion Points on CM Abelian Varieties2006
- Author(s)
  Noboru Aoki
- Journal Title
  
  Commentarii Mathematici Universitatis Sancti Pauli 55
  
  Pages: 207-229
- Data Source
  KAKENHI-PROJECT-18540055
[Journal Article] On Tate's refinement for a conjecture of Gross and its generalization2005
- Author(s)
  青木昇(Noboru Aoki)
- Journal Title
  
  J.Theorie des Nombres de Bordeaux. (To appear)
- Data Source
  KAKENHI-PROJECT-15540048
[Journal Article] The Hodge conjecture for the jacobian varieties of generalized Catalan curves2004
- Author(s)
  Noboru Aoki
- Journal Title
  
  Tokyo Journal of Mathematics 27
  
  Pages: 313-335
- Data Source
  KAKENHI-PROJECT-15540049
[Journal Article] A finiteness theorem on pure Gauss sums2004
- Author(s)
  青木昇(Noboru Aoki)
- Journal Title
  
  Comment.Math.Univ.Sancti Pauli 53
  
  Pages: 145-168
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-15540048
[Journal Article] The Hodge conjecture for the jacobian varieties of generalized Catalan curves2004
- Author(s)
  青木昇(Noboru Aoki)
- Journal Title
  
  Tokyo J.Math. 27
  
  Pages: 313-335
- Data Source
  KAKENHI-PROJECT-15540048
[Journal Article] On the Tate-Shafarevich groups of semistable elliptic curves with a rational 3-torsion2004
- Author(s)
  Noboru Aoki
- Journal Title
  
  Acta Arithmetica 112
  
  Pages: 209-227
- Data Source
  KAKENHI-PROJECT-15540049
[Journal Article] A finiteness theorem on pure Gauss sums2004
- Author(s)
  Noboru Aoki
- Journal Title
  
  Commentarii Mathematici Universitatis Sancti Pauli 53
  
  Pages: 145-168
- Data Source
  KAKENHI-PROJECT-15540049
[Journal Article] The Hodge conjecture for the jacobian varieties of generalized Catalan curves2004
- Author(s)
  N.Aoki
- Journal Title
  
  Tokyo J. Math. 27
  
  Pages: 313-335
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-15540049
[Journal Article] The Hodge conjecture for the jacobian varieties of generalized Catalan curves2004
- Author(s)
  青木昇(Noboru Aoki)
- Journal Title
  
  Tokyo J.Math. 27
  
  Pages: 313-335
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-15540048
[Journal Article] The Hodge conjecture for the jacobian varieties of generalized Catalan curves2004
- Author(s)
  N.Aoki
- Journal Title
  
  Tokyo J.Math. 27
  
  Pages: 313-335
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-15540049
[Journal Article] On the Tate-Shafarevich groups of semistable elliptic curves with a rational 3-torsion2004
- Author(s)
  青木昇(Noboru Aoki)
- Journal Title
  
  Acta Arithmetica 112
  
  Pages: 209-227
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-15540048
[Journal Article] A finiteness theorem on pure Gauss sums2004
- Author(s)
  Noboru Aoki
- Journal Title
  
  Comment.Math.Univ.Sancti Pauli
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-15540048
[Journal Article] On Tate's refinement for a conjecture of Gross and its generalization2004
- Author(s)
  N.Aoki
- Journal Title
  
  J. Theorie des Nombres de Bordeaux 16
  
  Pages: 457-486
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-15540049
[Journal Article] On the Tate-Shafarevich groups of semistable elliptic curves with a rational 3-torsion2004
- Author(s)
  N.Aoki
- Journal Title
  
  Acta Arithmetica 112
  
  Pages: 209-227
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-15540049
[Journal Article] The Hodge conjecture for the jacobian varieties of generalized Catalan curves2004
- Author(s)
  Noboru Aoki
- Journal Title
  
  Tokyo J.Math.
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-15540048
[Journal Article] A finiteness theorem on pure Gauss sums2004
- Author(s)
  N.Aoki
- Journal Title
  
  Comment. Math. Univ. Sancti Pauli 53
  
  Pages: 145-168
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-15540049
[Journal Article] On Tate's refinement for a conjecture of Gross and its generalization2004
- Author(s)
  N.Aoki
- Journal Title
  
  J.Theorie des Nombres de Bordeaux 16
  
  Pages: 457-486
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-15540049
[Journal Article] On the Tate-Shafarevich groups of semistable elliptic curves with a rational 3-torsion2004
- Author(s)
  Noboru Aoki
- Journal Title
  
  Acta Arithmetica
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-15540048
[Journal Article] A finiteness theorem on pure Gauss sums2004
- Author(s)
  N.Aoki
- Journal Title
  
  Comment.Math.Univ.Sancti Pauli 53
  
  Pages: 145-168
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-15540049
[Journal Article] On the generalized Gross-Tate conjecture for elementary abelian 2-extensions2003
- Author(s)
  青木昇(Noboru Aoki)
- Journal Title
  
  Comment.Math.Univ.Sancti Pauli 52
  
  Pages: 197-206
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-15540048
[Journal Article] On the generalized Gross-Tate conjecture for elementary abelian 2-extensions2003
- Author(s)
  Noboru Aoki
- Journal Title
  
  Comment.Math.Univ.Sancti Pauli
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-15540048

1. SHIODA Tetuji (00011627)

# of Collaborated Projects: 10 results

# of Collaborated Products: 0 results
2. FUJII Akio (50097226)

# of Collaborated Projects: 6 results

# of Collaborated Products: 0 results
3. SATO Fumihiro (20120884)

# of Collaborated Projects: 4 results

# of Collaborated Products: 0 results
4. 河井壮一 (40062624)

# of Collaborated Projects: 3 results

# of Collaborated Products: 0 results
5. 木田祐司 (30113939)

# of Collaborated Projects: 2 results

# of Collaborated Products: 0 results
6. MIYAOKA Yoichi (50101077)

# of Collaborated Projects: 2 results

# of Collaborated Products: 0 results
7. 栗原将人 (40211221)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
8. 中島晴久 (90145657)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
9. 佐々井崇雄 (00094269)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
10. 辻元 (30172000)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
11. 笹倉頌夫 (20087026)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
12. 卜部東介 (70145655)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
13. 荻上絋一 (10087025)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
14. UZAWA Tooru (40232813)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
15. YAMADA Yuuji (40287917)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
16. KUROKI Gen (10234593)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
17. HASEGAWA Kouji (30208483)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
18. ARAKAWA Tsuneo (60097219)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
19. ENDO Mikihiko (40062616)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
20. OHSUGI Hidefumi (80350289)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
21. KAKEI Saburo (60318798)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results

AOKI Noboru 青木 昇

青木 昇

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Research Institution

Studies on arithmetic problems on abelian varietiesPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Principal Investigator

Project Period (FY)

Research Category

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Principal Investigator

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Study on interrelations among quadratic forms, automorphic forms and related various zeta-functionsPrincipal Investigator

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Rational points on algebraic curves and its application to number theoryPrincipal Investigator

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アーベル多様体の算術的理論の研究Principal Investigator

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楕円曲線の算術的理論の研究Principal Investigator

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L関の特殊値の研究Principal Investigator

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AOKI Noboru 青木昇

青木昇