FUKUHARA Shinji 福原真二

… Alternative Names

福原真二フクハラシンジ

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Researcher Number	20011687
Other IDs
Affiliation (based on the past Project Information) *help	2014 – 2017: 津田塾大学, その他部局等, 名誉教授 2004 – 2013: 津田塾大学, 学芸学部, 教授 1997 – 2002: 津田塾大学, 学芸学部, 教授 1991: 津田塾大学, 学芸学部, 教授 1986 – 1989: 津田塾大学, 学芸学部, 教授 1987: 津田塾大学, 学芸学部・数学教室, 教授
Review Section/Research Field	Principal Investigator Geometry / Geometry / 代数学・幾何学 Except Principal Investigator Geometry / General mathematics (including Probability theory/Statistical mathematics) / 代数学・幾何学 / 解析学
Keywords	Principal Investigator 結び目 / 位相不変量 / デデキント和 / 保型形式 / 多様体 / 絡み目 / modular form / topological invariant / manifold / 周期多項式 … More / 結び目不変量 / knot / Dedekind sum / ヘッケ作用 / 周期 / 尖点形式 / period polynomial / Hecke operator / 周期積分 / elliptic function / link / 楕円関数 / Jacobi form / Dedekind sums / low dimensional manifold / ヤコビ形式 / 低次元多様体 / ホモロジー球面 / 三次元多様体 / 曲線の自己交差 / 相互法則 / カウフマン多項式 / ジョーンズ多項式 / ベルヌーイ数 / 曲面上の曲線 / 一般デデキント和 / L-関数 / 楕円デデキント和 / 局所変形 / 不変量 / 位相幾何学 / ヘッケ作用素 / 位相幾何 / トポロジ- … More Except Principal Investigator monodromy / モノドロミー / splitting / singular fiber / degeneration / Riemann surfaces / 擬周期写像 / 同伴不等式 / カンドル / 大域モノドロミー / Seiberg-witten方程式 / 分裂変形 / クアンドル / 大域的モノドロミー / 分裂 / 特異ファイバー / 退化 / リーマン面 / braid group / Lefschetz fibration / racks / ブレイド群 / レフシェツ・ファイバー空間 / ラック / 完全交叉ミルナーファイバーの指数 / ザイフェルト多様体 / ホモロジー球面 / ラムダ不変量 / カオス / ハミルトン系 / 無限粒子系 / ディオファンタス近似 / フラクタル / 複素数 / 10進展開 / フラクタル曲線 / 自己準同型 / 自由群 / ワ-クステ-ション / CAI Less

Topological invariants of manifolds, modular forms and Dedekind symbolsPrincipal Investigator
- Principal Investigator
  
  Fukuhara Shinji
- Project Period (FY)
  2014 – 2017
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Tsuda University
Knot invariants, modular forms and elliptic Dedekind sumsPrincipal Investigator
- Principal Investigator
  
  FUKUHARA SHINJI
- Project Period (FY)
  2010 – 2013
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Tsuda College
Study on Hecke operators for cusp forms and topological invariantsPrincipal Investigator
- Principal Investigator
  
  FUKUHARA Shinji
- Project Period (FY)
  2007 – 2009
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Tsuda College
Modular forms and Dedekind symbols as topological invariantsPrincipal Investigator
- Principal Investigator
  
  FUKUHARA Shinji
- Project Period (FY)
  2004 – 2006
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Tsuda College
Topological Study on the Degeneration Phenomena of Riemann Surfaces
- Principal Investigator
  
  MATSUMOTO Yukio
- Project Period (FY)
  2000 – 2002
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Geometry
- Research Institution
  The University of Tokyo
Topological invariants of manifolds and modular formsPrincipal Investigator
- Principal Investigator
  
  FUKUHARA Shinji
- Project Period (FY)
  2000 – 2002
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Tsuda College
Monodromy calculus in low dimensional topology and "racks".
- Principal Investigator
  
  MASUMOTO Yuki
- Project Period (FY)
  1998 – 1999
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Geometry
- Research Institution
  The University of Tokyo
Invariants of 3-manifolds and Dedekind sumsPrincipal Investigator
- Principal Investigator
  
  FUKUHARA Shinji
- Project Period (FY)
  1997 – 1998
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Tsuda College
結び目と三次元多様体論Principal Investigator
- Principal Investigator
  
  福原真二
- Project Period (FY)
  1991
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  代数学・幾何学
- Research Institution
  Tsuda College
CAIを利用した数学教育の研究
- Principal Investigator
  
  小川貴英
- Project Period (FY)
  1989
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  General mathematics (including Probability theory/Statistical mathematics)
- Research Institution
  Tsuda College
特異点の位相
- Principal Investigator
  
  坂本幸一
- Project Period (FY)
  1988
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  代数学・幾何学
- Research Institution
  Tsuda College
3, 4次元多様体の位相構造Principal Investigator
- Principal Investigator
  
  福原真二
- Project Period (FY)
  1987
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  代数学・幾何学
- Research Institution
  Tsuda College
Hamilton系のエルゴード問題とその周辺
- Principal Investigator
  
  丹羽敏雄
- Project Period (FY)
  1987
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  General mathematics (including Probability theory/Statistical mathematics)
- Research Institution
  Tsuda College
代数的多様体上の微分方程式
- Principal Investigator
  
  大槻真
- Project Period (FY)
  1986
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  解析学
- Research Institution
  Tsuda College

All 2017 2015 2014 2013 2012 2010 2009 2008 2007 2006 2005 2004 Other

All Journal Article Presentation

[Journal Article] Kauffman-Jones polynomial of a curve on a surface2017
- Author(s)
  Fukuhara Shinji、Kuno Yusuke
- Journal Title
  
  Journal of Knot Theory and Its Ramifications
  
  Volume: 26 Issue: 11 Pages: 1750062-1750078
- DOI
  10.1142/s0218216517500626
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-26400098, KAKENHI-PROJECT-26800044
[Journal Article] Generating functions of even Dedekind symbols with polynomial reciprocity laws2014
- Author(s)
  Shinji Fukuhara
- Journal Title
  
  Abh. Math. Semin. Univ. Hambg.
  
  Volume: 84 Issue: 2 Pages: 139-153
- DOI
  10.1007/s12188-014-0096-4
- Peer Reviewed / Acknowledgement Compliant
- Data Source
  KAKENHI-PROJECT-26400098
[Journal Article] Bases for S_k(¥Gamma_1(4)) and formulas for even powers of the Jacobi theta function2013
- Author(s)
  Shinji Fukuhara, Yifan Yang
- Journal Title
  
  Int. J. Number Thoery
  
  Volume: 9 Pages: 1973-1993
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22540096
[Journal Article] Bases for S_k(\Gamma_1(4)) and formulas for even powers of the Jacobi theta function2013
- Author(s)
  Shinji Fukuhara, Yifan Yang
- Journal Title
  
  Int. J. Number Theory
  
  Volume: 9 Issue: 08 Pages: 1973-1993
- DOI
  10.1142/s1793042113500693
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22540096
[Journal Article] A basis for S_k(Gamma_0(4)) and representations of integers as sums of squares2012
- Author(s)
  Shinji Fukuhara, Yifan Yang
- Journal Title
  
  Ramanujan J
  
  Volume: 28 Pages: 25-43
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22540096
[Journal Article] A basis for S_k(¥Gamma_0(4)) and representations of integers as sums of squares2012
- Author(s)
  Shinji Fukuhara, Yifan Yang
- Journal Title
  
  Ramanujan J.
  
  Volume: 28 Pages: 25-43
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22540096
[Journal Article] A basis for the space of modular forms2012
- Author(s)
  Shinji Fukuhara
- Journal Title
  
  Acta Arith.
  
  Volume: 151 Pages: 421-427
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22540096
[Journal Article] A basis for S_k(Gamma_0(4)) and representations of integers as sums of squares2012
- Author(s)
  Shinji Fukuhara
- Journal Title
  
  Ramanujan J.
  
  Volume: 28 Issue: 1 Pages: 25-43
- DOI
  10.1007/s11139-011-9341-y
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22540096
[Journal Article] A basis for the space of modular forms2012
- Author(s)
  Shinji Fukuhara
- Journal Title
  
  Acta Arithmetica
  
  Volume: 151 Pages: 421-427
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22540096
[Journal Article] Twisted Hecke L-values and period polynomials2010
- Author(s)
  Shinji Fukuhara, Yifan Yang
- Journal Title
  
  J. Number Theory
  
  Volume: 130 Pages: 976-999
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22540096
[Journal Article] The elliptic Apostol-Dedekind sums generate odd Dedekind symbols with Laurent polynomial reciprocity laws2010
- Author(s)
  Shinji Fukuhara
- Journal Title
  
  Math. Ann.
  
  Volume: 346 Pages: 769-794
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22540096
[Journal Article] Twisted Hecke L-value and period polynomials2010
- Author(s)
  Shinji Fukuhara
- Journal Title
  
  J.Number Theory 130
  
  Pages: 976-999
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19540101
[Journal Article] Twisted Hecke L-values and period polynomials2010
- Author(s)
  Shinji Fukuhara
- Journal Title
  
  J.Number Theory
  
  Volume: 130 Pages: 976-999
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22540096
[Journal Article] The elliptic Apostol-Dedekind sums generate odd Dedekind symbols with Laurent polynomial reciprocity laws2010
- Author(s)
  Shinji Fukuhara
- Journal Title
  
  Math.Ann.
  
  Volume: 346 Pages: 769-794
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22540096
[Journal Article] The elliptic Apostol-Dedekind sums generate odd Dedekind symbols with Laurent polynomial reciprocity laws2010
- Author(s)
  Shinji Fukuhara
- Journal Title
  
  Math. Ann 346
  
  Pages: 769-794
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19540101
[Journal Article] Period polynomials and explicit formulas for Hecke operators on \Garama_0(2)2009
- Author(s)
  Shinji Fukuhara Yifan Yang
- Journal Title
  
  Math. Proc. Cambridge Philos. Soc. 146
  
  Pages: 321350-321350
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19540101
[Journal Article] Period polynomials and explicit formulas for Hecke operators on \Gamma_0(2)2009
- Author(s)
  Shinji Fukuhara, Yifan Yang
- Journal Title
  
  Proc. Cambridge Philos. Soc. 146
  
  Pages: 321-350
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19540101
[Journal Article] Dedekind symbols with plus reciprocity laws2008
- Author(s)
  Shinji Fukuhara
- Journal Title
  
  J. Number Theory 128
  
  Pages: 781-795
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19540101
[Journal Article] Explicit formulas for Hecke operators on cusp forms, Dedekind symbols and period polynomials2007
- Author(s)
  Shinji Fukuhara
- Journal Title
  
  J. Reine Angew. Math 607
  
  Pages: 163-216
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19540101
[Journal Article] Explicit formulas for Hecke operators on cusp forms, Dedekind symbols and period polynomials2007
- Author(s)
  Shinji Fukuhara
- Journal Title
  
  J. refine angew. Math. 607
  
  Pages: 163-216
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19540101
[Journal Article] Hecke operators on weighted Dedekind symbols2006
- Author(s)
  Shinji Fukuhara
- Journal Title
  
  J. reine angew. Math. 593
  
  Pages: 1-29
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-16540081
[Journal Article] Hecke operators on weighted Dedekind symbols2006
- Author(s)
  Shinji Fukuhara
- Journal Title
  
  J. reine angew, Math. 593
  
  Pages: 1-29
- Data Source
  KAKENHI-PROJECT-16540081
[Journal Article] A generating function of higher-dimensional Apostol-Zagier sums and its reciprocity law2006
- Author(s)
  Shinji Fukuhara, Noriko Yui
- Journal Title
  
  J.Number Theory 117
  
  Pages: 87-105
- Data Source
  KAKENHI-PROJECT-16540081
[Journal Article] A generating function of higher-dimensional Apostol-Zagier sums and its reciprocity law2006
- Author(s)
  Shinji Fukuhara
- Journal Title
  
  J. Number Theory 117
  
  Pages: 87-105
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-16540081
[Journal Article] The Dedekind symbol associated with the Eisenstein series of weight two2005
- Author(s)
  Shinji Fukuhara
- Journal Title
  
  Arch. Math. 85
  
  Pages: 128-140
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-16540081
[Journal Article] The Dedekind symbol associated with the Eisenstein series of weight two2005
- Author(s)
  Shinji Fukuhara, Noriko Yui
- Journal Title
  
  Arch.Math. 85
  
  Pages: 128-140
- Data Source
  KAKENHI-PROJECT-16540081
[Journal Article] Explicit formulae for two-bridge knot polynomials2005
- Author(s)
  Shinji Fukuhara
- Journal Title
  
  J. Aust. Math. Soc. 78
  
  Pages: 149-166
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-16540081
[Journal Article] Explicit formulae for two-bridge knot polynomials2005
- Author(s)
  Shinji Fukuhara
- Journal Title
  
  J.Aust.Math.Soc. 78
  
  Pages: 149-166
- Data Source
  KAKENHI-PROJECT-16540081
[Journal Article] Dedekind symbols with polynomial reciprocity laws2004
- Author(s)
  Shinji Fukuhara
- Journal Title
  
  Math.Ann. 329
  
  Pages: 315-334
- Data Source
  KAKENHI-PROJECT-16540081
[Journal Article] Elliptic Apostol sums and their reciprocity laws2004
- Author(s)
  Shinji Fukuhara, Noriko Yui
- Journal Title
  
  Trans.Amer.Math.Soc. 356
  
  Pages: 4237-4254
- Data Source
  KAKENHI-PROJECT-16540081
[Journal Article] Elliptic Apostol sums and their reciprocity laws2004
- Author(s)
  Shinji Fukuhara
- Journal Title
  
  Trans. Amer. Math. Soc. 356
  
  Pages: 4237-4254
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-16540081
[Journal Article] Dedekind symbols with polynomial reciprocity laws2004
- Author(s)
  Shinji Fukuhara
- Journal Title
  
  Math. Ann. 329
  
  Pages: 315-334
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-16540081
[Journal Article] Explicit formulas for Hecke operators on cusp forms, Dedekind symbols and period polynomials
- Author(s)
  Shinji Fukuhara
- Journal Title
  
  J. reine angew. Math. (印刷中)
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-16540081
[Journal Article] Explicit formulas for Hecke operators on cups forms, Dedekind symbols and period polynomials
- Author(s)
  Shinji Fukuhara
- Journal Title
  
  J. reine angew, Math. (印刷中)
- Data Source
  KAKENHI-PROJECT-16540081
[Journal Article] Explicit formulas for Hecke operators on cusp forms, Dedekind symbols and period polynomials
- Author(s)
  Shinji Fukuhara
- Journal Title
  
  J. reine angew. Math.
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-16540081
[Presentation] Dedekind symbolと保型形式2015
- Author(s)
  福原真二
- Organizer
  リーマン面に関する位相幾何学2015
- Place of Presentation
  東京大学数理科学研究科大講義室
- Year and Date
  2015-08-25
- Data Source
  KAKENHI-PROJECT-26400098

1. SAKAMOTO Koichi (40090518)

# of Collaborated Projects: 7 results

# of Collaborated Products: 0 results
2. MIYAZAWA Haruko (40266276)

# of Collaborated Projects: 5 results

# of Collaborated Products: 0 results
3. 大槻真 (20110348)

# of Collaborated Projects: 2 results

# of Collaborated Products: 0 results
4. 伊藤俊次 (30055321)

# of Collaborated Projects: 2 results

# of Collaborated Products: 0 results
5. 太田香 (60147006)

# of Collaborated Projects: 2 results

# of Collaborated Products: 0 results
6. 三鳥川寿一 (80055318)

# of Collaborated Projects: 2 results

# of Collaborated Products: 0 results
7. 森光弥 (90055278)

# of Collaborated Projects: 2 results

# of Collaborated Products: 0 results
8. 片山孝次 (10055296)

# of Collaborated Projects: 2 results

# of Collaborated Products: 0 results
9. MASUMOTO Yuki (20011637)

# of Collaborated Projects: 2 results

# of Collaborated Products: 0 results
10. KAMADA Seiichi (60254380)

# of Collaborated Projects: 2 results

# of Collaborated Products: 0 results
11. 小川貴英 (60011227)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
12. 長岡一昭 (60119550)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
13. 渡辺隼郎 (00055310)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
14. 丹羽敏雄 (70025419)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
15. 安藤茂 (40147004)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
16. 田中茂 (70055317)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
17. KAWAUCHI Akio (00112524)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
18. OHTSUKI Tomotada (50223871)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
19. IMAYOSHI Yoichi (30091656)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
20. ASHIKAGA Tadashi (90125203)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
21. AHARA Kazushi (80247147)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
22. KAWAZUMI Nariya (30214646)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
23. 古田幹雄 (50181459)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results

FUKUHARA Shinji 福原 真二

福原 真二 フクハラ シンジ

Research Projects

Research Products

Co-Researchers

Topological invariants of manifolds, modular forms and Dedekind symbolsPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Knot invariants, modular forms and elliptic Dedekind sumsPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Study on Hecke operators for cusp forms and topological invariantsPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Modular forms and Dedekind symbols as topological invariantsPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Topological Study on the Degeneration Phenomena of Riemann Surfaces

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Topological invariants of manifolds and modular formsPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Monodromy calculus in low dimensional topology and "racks".

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Invariants of 3-manifolds and Dedekind sumsPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

結び目と三次元多様体論Principal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

CAIを利用した数学教育の研究

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

特異点の位相

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

3, 4次元多様体の位相構造Principal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Hamilton系のエルゴード問題とその周辺

Principal Investigator

Project Period (FY)

FUKUHARA Shinji 福原真二

福原真二フクハラシンジ