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Research on geometry related to theta functions

Research Project

Project/Area Number 17540001
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionHokkaido University

Principal Investigator

MATSUMOTO Keiji  Hokkaido University, 大学院・理学研究院, 教授 (30229546)

Co-Investigator(Kenkyū-buntansha) ONO Kaoru  北海道大学, 大学院・理学研究院, 教授 (20204232)
NAKAMURA Iku  北海道大学, 大学院・理学研究院, 教授 (50022687)
SHIMADA Ichiro  北海道大学, 大学院・理学研究院, 准教授 (10235616)
IWASAKI Katsunori  九州大学, 大学院・数理学研究院, 教授 (00176538)
TERASOMA Tomohide  東京大学, 大学院・数理科学研究科, 教授 (50192654)
YOSHIDA Masaaki  九州大学, 大学院・数理学研究院, 教授 (30030787)
Co-Investigator(Renkei-kenkyūsha) ONO Kaoru  北海道大学, 大学院・理学研究院, 教授 (20204232)
NAKAMURA Iku  北海道大学, 大学院・理学研究院, 教授 (50022687)
IWASAKI Katsunori  九州大学, 大学院・数理学研究院, 教授 (00176538)
SHIMADA Ichiro  広島大学, 大学院・理学研究科, 教授 (10235616)
TERASOMA Tomohide  東京大学, 大学院・数理科学研究科, 教授 (50192654)
YOSHIDA Masaaki  九州大学, 大学院・数理学研究院, 教授 (30030787)
Project Period (FY) 2005 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥3,850,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥450,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2006: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2005: ¥1,200,000 (Direct Cost: ¥1,200,000)
Keywordsテータ関数 / 超幾何関数 / 双曲幾何 / 算術幾何平均 / 平均反復 / モジュライ空間 / 双曲空間
Research Abstract

テータ関数や超幾何関数のみたす関数等式を多数与えた。テータ関数のみたす関数等式によりWhitehead link と Borromean ringsの補空間に入る双曲構造を解明した。また、超幾何関数のみたす関数等式より、いくつかの多項版の算術幾何平均を定め、それらの値の表示公式を与えた。

Report

(5 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • 2005 Annual Research Report
  • Research Products

    (38 results)

All 2009 2008 2007 2006 2005 Other

All Journal Article (22 results) (of which Peer Reviewed: 12 results) Presentation (14 results) Book (2 results)

  • [Journal Article] Automorphic forms on the $5$-dimensionalcomplex ball with respect to the Picardmodular group over Z [i]2007

    • Author(s)
      K. Matsumoto, T. Minowa and R.Nishimura
    • Journal Title

      Hokkaido Math. J 36

      Pages: 143-173

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Automorphic forms on the $5$-dimensional complex ball with respect to the Picard modular group over Z[i]2007

    • Author(s)
      K. Matsumoto, T. Minowa, R. Nishimura
    • Journal Title

      Hokkaido Math. J. 36

      Pages: 143-173

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Automorphic functions for the Whitehead-link-complement group2006

    • Author(s)
      K. Matsumoto, H. Nishi and M. Yoshida
    • Journal Title

      Osaka J. Math 43

      Pages: 839-876

    • NAID

      120004842011

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Automorphic functions with respect to thefundamental group of the complement ofthe Borromean rings2006

    • Author(s)
      Keiji Matsumoto
    • Journal Title

      J. Math. Sci. Univ. Tokyo 13

      Pages: 1-11

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Algebraic relations among theta functionson the bounded symmetric domain of typeI_{r,r}2006

    • Author(s)
      Keiji Matsumoto
    • Journal Title

      Kyushu J. Math 60

      Pages: 63-77

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Attempts to construct automorphicfunctions for hyperbolic links2006

    • Author(s)
      Keiji Matsumoto
    • Journal Title

      双曲空間の複素解析と幾何学的研究, 数理研講究録 1518

      Pages: 76-86

    • Related Report
      2008 Final Research Report
  • [Journal Article] Algebraic relations among theta functions on the bounded symmetric domain of type Ir, r2006

    • Author(s)
      K.Matsumoto
    • Journal Title

      Kyushu J. Math. 60・1

      Pages: 63-77

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Automorphic functions with respect to the fundamental group of the complement of the Borromean rings2006

    • Author(s)
      K.Matsumoto
    • Journal Title

      J. Math. Sci. Univ. Tokyo, 13

      Pages: 1-11

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Automorphic functions for the Whitehead-link-complement group2006

    • Author(s)
      K.Matsumoto
    • Journal Title

      Osaka J. Math. 43

      Pages: 839-876

    • NAID

      120004842011

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Attempts to construct automorphic functions for hyperbolic links2006

    • Author(s)
      K.Matsumoto
    • Journal Title

      数理研講究録 1518

      Pages: 76-86

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Algebraic relations among some theta functions on the bounded symmetric domain of type I_<r,r>2006

    • Author(s)
      K.Matsumoto
    • Journal Title

      Kyushu J.Math. (掲載予定)

    • NAID

      130000063156

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Automorphic forms on the 5-dimensional complex ball with respect to the Picard modular group over Z[i]2006

    • Author(s)
      K.Matsumoto
    • Journal Title

      Hokkaido Math.J. (掲載予定)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Moduli curves of supersingular K3 surfaces in characteristic 2 with Artin invariant 22006

    • Author(s)
      I.Shimada
    • Journal Title

      Proc.Edinb.Math.Soc. (掲載予定)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Simple singularities and symplectic fillings2005

    • Author(s)
      K.Ono
    • Journal Title

      J.Differential Geom. 69,1

      Pages: 1-42

    • Related Report
      2005 Annual Research Report
  • [Journal Article] 周期積分と多重ゼータ値2005

    • Author(s)
      寺杣 友秀
    • Journal Title

      数学 57,3

      Pages: 255-266

    • NAID

      10017177123

    • Related Report
      2005 Annual Research Report
  • [Journal Article] The common limit of a quadruplesequence and the hypergeometric function F_D of three variables

    • Author(s)
      T. Kato and K. Matsumoto
    • Journal Title

      Nagoya Math. J (掲載決定)

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Arithmetic-geometric means forhyperelliptic curves and Calabi-Yauvarieties

    • Author(s)
      K. Matsumoto and T. Terasoma
    • Journal Title

      Internat. J. Math (掲載決定)

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Some transformation formulas for Lauricella's hypergeometric function F_D

    • Author(s)
      K. Matsumoto and K. Ohara
    • Journal Title

      Funkcial. Ekvac (掲載決定)

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Mean iterations derived fromtransformation formulas for thehypergeometric function

    • Author(s)
      R. Hattori, T. Kato and K. Matsumoto
    • Journal Title

      Hokkaido Math. J (掲載決定)

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Some transformation formulas for Lauricella's hypergeometric functions F_D

    • Author(s)
      Keiji Matsumoto, Katsuyoshi Ohara
    • Journal Title

      Funkcial. Ekvac (掲載決定)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Arithmetic-geometric means for hyperelliptic curves and Calabi-Yau varieties

    • Author(s)
      Keiji Matsumoto, Tomohida Terasoma
    • Journal Title

      Internat. J. Math (掲載決定)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The common limit of a quadruple sequence and the hypergeometric function F_D of three variables

    • Author(s)
      Takayuki Kato, Keiji Matsumoto
    • Journal Title

      Nagoya Math. J. (掲載決定)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] 超幾何関数の変換公式と平均反復2009

    • Author(s)
      松本圭司
    • Organizer
      計算による数理科学の展開 2009
    • Place of Presentation
      神戸大学
    • Year and Date
      2009-01-08
    • Related Report
      2008 Final Research Report
  • [Presentation] Formulas of Thomae type and MeanIterations2008

    • Author(s)
      松本圭司
    • Organizer
      テータ関数と可積分系
    • Place of Presentation
      九州大学
    • Year and Date
      2008-12-21
    • Related Report
      2008 Final Research Report
  • [Presentation] Some Analogies to the Relation between AGMand the Hypergeometric Function,-Hypergeometric Functions and Mean Iterations -Geometry and Arithmetic aroundHypergeometric Functions2008

    • Author(s)
      Keiji Matsumoto
    • Organizer
      Mathematisches Forschungsinstitut Oberwolfach
    • Place of Presentation
      Germany
    • Year and Date
      2008-10-02
    • Related Report
      2008 Final Research Report
  • [Presentation] Some Analogies to the Relation between AGM and the Hype rgeometric Function2008

    • Author(s)
      Keiji Matsumoto
    • Organizer
      Geometry and Arithmetic around Hypergeometric Functions
    • Place of Presentation
      Mathematisches Forschungsinstitut Oberwolfach
    • Year and Date
      2008-10-02
    • Related Report
      2008 Annual Research Report
  • [Presentation] 算術幾何平均の拡張への試み2008

    • Author(s)
      服部良平, 加藤孝幸, 松本圭司
    • Organizer
      超幾何方程式研究会2008
    • Place of Presentation
      神戸大学
    • Year and Date
      2008-01-07
    • Related Report
      2008 Final Research Report
  • [Presentation] ある4項算術幾何平均と3変数超幾何関数2007

    • Author(s)
      松本圭司
    • Organizer
      アクセサリー・パラメーター研究会
    • Place of Presentation
      熊本大学
    • Year and Date
      2007-10-09
    • Related Report
      2008 Final Research Report
  • [Presentation] ある4項算術幾何平均と3変数超幾何関数2007

    • Author(s)
      松本 圭司
    • Organizer
      アクセサリー・パラメーター研究会
    • Place of Presentation
      熊本大学大学院自然科学研究科
    • Year and Date
      2007-10-09
    • Related Report
      2007 Annual Research Report
  • [Presentation] 三輪絡み目補空間の逆黒写像2006

    • Author(s)
      松本圭司
    • Organizer
      アクセサリー・パラメーター研究会
    • Place of Presentation
      熊本大学
    • Year and Date
      2006-06-20
    • Related Report
      2008 Final Research Report
  • [Presentation] ζ関数の周期関係式2006

    • Author(s)
      松本圭司
    • Organizer
      超幾何方程式研究会2006
    • Place of Presentation
      神戸大学
    • Year and Date
      2006-01-06
    • Related Report
      2008 Final Research Report
  • [Presentation] Automorphic functions for the Borromean-rings-complement group2005

    • Author(s)
      Keiji Matsumoto
    • Organizer
      双曲空間の複素解析と幾何学的研究
    • Place of Presentation
      京大数理研
    • Year and Date
      2005-12-07
    • Related Report
      2008 Final Research Report
  • [Presentation] 双曲絡み目保型関数の試作品2005

    • Author(s)
      松本圭司
    • Organizer
      日本数学会秋季年会特別講演
    • Place of Presentation
      岡山大学
    • Year and Date
      2005-09-20
    • Related Report
      2008 Final Research Report
  • [Presentation] 超幾何関数の幾何学-交点理論2005

    • Author(s)
      松本圭司
    • Organizer
      多変数関数論サマーセミナー
    • Place of Presentation
      湯沢グランドホテル
    • Year and Date
      2005-08-01
    • Related Report
      2008 Final Research Report
  • [Presentation] Invariant functions with respect to the Whitehead link Arithmetic and Geometry around Hypergeometric Functions2005

    • Author(s)
      Keiji Matsumoto
    • Organizer
      CIMPA-Istanbul AGAHF 2005, Galatasaray University, Istanbul
    • Place of Presentation
      Turkey
    • Year and Date
      2005-06-22
    • Related Report
      2008 Final Research Report
  • [Presentation] Automorphic functions for the Whitehead-link2005

    • Author(s)
      Keiji Matsumoto
    • Organizer
      Integrable Systems, Geometry, and Abelian Functions
    • Place of Presentation
      首都大学
    • Year and Date
      2005-05-26
    • Related Report
      2008 Final Research Report
  • [Book] Progr. Math., 260, Edited by R.P. Holzapfel, A. Muhammed Uludag and M. Yoshida, Birkhauser Verlag Basel2007

    • Author(s)
      Keiji Matsumoto
    • Publisher
      Arithmetic and geometry aroundhypergeometric functions, Invariantfunctions with respect to the Whitehead-Link
    • Related Report
      2008 Final Research Report
  • [Book] Arithmetic and geometry around hypergeometric functions, Progr. Math., 260 Edited by R.P. Holzapfel A. Muhammed Uludag and M. Yoshida2007

    • Author(s)
      K. Matsumoto
    • Publisher
      Birkhauser
    • Related Report
      2007 Annual Research Report

URL: 

Published: 2005-04-01   Modified: 2016-04-21  

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