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Refined Iwasawa theory and the zeta functions

Research Project

Project/Area Number 17340010
Research Category

Grant-in-Aid for Scientific Research (B)

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

Principal Investigator

KURIHARA Masato  Keio University, 理工学部, 教授 (40211221)

Co-Investigator(Kenkyū-buntansha) OTA Katsuhiro  慶應義塾大学, 理工学部, 教授 (40213722)
TANAKA Takaaki  慶應義塾大学, 理工学部, 助教 (60306850)
MIYAZAKI Takuya  慶應義塾大学, 理工学部, 准教授 (10301409)
SHIOKAWA Iekata  慶應義塾大学, 理工学部, 名誉教授 (00015835)
BANNAI Kenichi  慶應義塾大学, 理工学部, 講師 (90343201)
松野 一夫  津田塾大学, 学芸学部, 准教授 (40332936)
藤井 俊  慶應義塾大学, 大学院・理工学研究科, 特別研究助教 (20386618)
落合 理  大阪大学, 大学院・理学研究科, 講師 (90372606)
加藤 和也  京都大学, 大学院・理学研究科, 教授 (90111450)
Co-Investigator(Renkei-kenkyūsha) MATSUNO Kazuo  津田塾大学, 学芸学部, 准教授 (40332936)
HACHIMORI Yoshitaka  東京理科大学, 理工学部, 講師 (50433743)
AOKI Miho  岡山理科大学, 理学部, 講師 (10381451)
Project Period (FY) 2005 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥9,710,000 (Direct Cost: ¥8,600,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2008: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2007: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2006: ¥1,900,000 (Direct Cost: ¥1,900,000)
Fiscal Year 2005: ¥3,000,000 (Direct Cost: ¥3,000,000)
Keywords整数論 / 岩澤理論 / 岩澤主予想 / Fittingイデアル / Kolyvagin系 / 国際研究者交流 / ドイツ:韓国 / Euler系 / Stickelberger元 / 楕円曲線 / p進L関数 / 有理点
Research Abstract

従来の岩澤理論では、岩澤主予想という、数論的対象物へのGalois群の作用の特性多項式とp進L関数との関係、が主テーマであったが、数論的対象物と解析的対象物との間にはもっと深い関係があることが証明できた。また、Gauss和型のEuler系の理論、Gauss和型のKolyvagin系の理論を構成し、Galoisコホモロジーの中にゼータ関数の値と関係するよい元の系列が存在することを証明した。

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

    (36 results)

All 2009 2008 2007 2006 2005 Other

All Journal Article (26 results) (of which Peer Reviewed: 16 results) Presentation (10 results)

  • [Journal Article] Stickelberger elements, Fitting ideals of class groups of CM fields, and dualisation2008

    • Author(s)
      Cornelius Greither and Masato Kurihara
    • Journal Title

      Mathematische Zeitschrift 260

      Pages: 905-930

    • Related Report
      2008 Final Research Report
  • [Journal Article] On the 2-adic Iwasawa invariants of ordinary elliptic curves2008

    • Author(s)
      Kazuo Matsuno
    • Journal Title

      International Journal of Number Theory 4

      Pages: 403-422

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Remarkable algebraic independence property of certain series related to continued fractions2008

    • Author(s)
      Taka-aki Tanaka
    • Journal Title

      Diophantine analysis and related fields-DARF 2007/2008, AIP Conf. Proc 976, Melville, NY

      Pages: 190-204

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Stickelberger elements, Fitting ideals of class groups of CM fields, and dualisation2008

    • Author(s)
      C. Greither, Masato Kurihara
    • Journal Title

      Mathematische Zeitschrift 260

      Pages: 905-930

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Remarkable algebraic independence property of certain series related to continued fractions2008

    • Author(s)
      Taka-aki Tanaka
    • Journal Title

      Diophantine analysis and related fields---DARF 2007/2008, AIP Conf. Proc 976

      Pages: 190-204

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Pattern sequences in <q, r>-numneration systems2008

    • Author(s)
      Iekata Shiokawa, Yohei Tachiya
    • Journal Title

      Indagationes Mathematicae 19

      Pages: 151-161

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The torsion of p-ramified Iwasawa modules2008

    • Author(s)
      Satoshi Fujii
    • Journal Title

      Proc.Amer.Math.Soc 136

      Pages: 461-466

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Two p-adic L-functions and rational points on elliptic curves with supersingular reduction, London Math2007

    • Author(s)
      Masato Kurihara and Robert Pollack
    • Journal Title

      Society Lecture Note Series 320

      Pages: 300-332

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Construction of elliptic curves with large Iwasawa lambda- invariants and large Tate-Shafarevich groups2007

    • Author(s)
      Kazuo Matsuno
    • Journal Title

      Manuscripta Math 122

      Pages: 289-304

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Algebraic theta functions and Eisenstein-Kronecker numbers2007

    • Author(s)
      Ken-ichi Bannai and Shin-ichi Kobayashi
    • Journal Title

      RIMS Kokyuroku Bessatsu B4

      Pages: 63-77

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Two p-adic L-functions and rational points on elliptic curves with supersingular reduction2007

    • Author(s)
      Masato Kurihara and Robert Pollack
    • Journal Title

      London Mathematical Society Lecture Note Series 320

      Pages: 300-332

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Construction of elliptic curves with large Iwasawa lambda-invariants and large Tate-Shafarevich groups2007

    • Author(s)
      Kazuo Matsuno
    • Journal Title

      Manuscripta Mathematica 122

      Pages: 289-304

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the growth of Selmer groups of an elliptic curve with supersingular reduction in the Z_{2}-extension of Q2006

    • Author(s)
      Masato Kurihara and Rei Otsuki
    • Journal Title

      Pure and Applied Mathematics Quaterly 2

      Pages: 557-568

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Algebraic indep-endence of modified reciprocal sums of products of Fibonacci numbers2006

    • Author(s)
      Taka-aki Tanaka
    • Journal Title

      Tsukuba J. Math 30

      Pages: 345-361

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the growth of Selmer groups of an elliptic curve With supersingular reduction2006

    • Author(s)
      Masato Kurihara, Rei Otsuki
    • Journal Title

      Pure and Applied Math Quarterly Volume 2 Number 2

      Pages: 557-568

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Construction of Z_p-extensions with prescribed Iwasawa $lambda$-invariants2006

    • Author(s)
      Satoshi Fujii, Y. Ohgi, M. Ozaki
    • Journal Title

      Journal of Number Theory Vol. 118 No. 2

      Pages: 200-207

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Algebraic independence of modified reciprocal sums of products of Fibonacci numbers2006

    • Author(s)
      Taka-aki Tanaka
    • Journal Title

      Tsukuba Journal Math. Vol. 30 No. 2

      Pages: 345-361

    • NAID

      120005366087

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Remarks on the lambda_p-invariants of cyclic fields of degree p2005

    • Author(s)
      Masato Kurihara
    • Journal Title

      Acta Arithmetica 116

      Pages: 199-216

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the failure of pseudo-nullity of Iwasawa modules, J2005

    • Author(s)
      Yoshitaka Hachimori and Romyar Sharifi
    • Journal Title

      Algebraic Geometry 14

      Pages: 567-591

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Algebraic indep- endence of the values of power series2005

    • Author(s)
      Taka-aki Tanaka
    • Journal Title

      Lambert series, and infinite products generated by linear recurrences, Osaka J. Math 42

      Pages: 487-497

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Remarks on the lambda_{p}-invariants of cyclic fields of degree p2005

    • Author(s)
      Masato Kurihara
    • Journal Title

      Acta Arithmetica 116

      Pages: 199-216

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Euler system for Galois deformations2005

    • Author(s)
      Tadashi Ochiai
    • Journal Title

      Ann.Inst. Fourier (Grenoble) 55

      Pages: 113-146

    • Related Report
      2005 Annual Research Report
  • [Journal Article] On a higher class number formula of Z_{p}-extensions2005

    • Author(s)
      Satoshi Fujii
    • Journal Title

      Tokyo Journal of Mathematics 28

      Pages: 55-61

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Algebraic independence of the values of power series, Lambert series, and infinite products generated by linear recurrences2005

    • Author(s)
      Tanaka Taka-aki
    • Journal Title

      Osaka Journal of Mathematics 42

      Pages: 487-497

    • NAID

      120004845247

    • Related Report
      2005 Annual Research Report
  • [Journal Article] K_{1} of some non-commutative completed group rings2005

    • Author(s)
      Kazuya Kato
    • Journal Title

      K-theory 34

      Pages: 99-140

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Two p-adic L-functions and rational points on elliptic curves with supersingular reduction

    • Author(s)
      Masato Kurihara, Robert Pollack
    • Journal Title

      Proceedings for the Durham conference on Number Theory (Cambridge Univ Press)(出版確定)

    • Related Report
      2006 Annual Research Report
  • [Presentation] On the Stickelberger ideals for cyclotomic fields2009

    • Author(s)
      Masato Kurihara
    • Organizer
      The 14th Joint Workshop on Number Theory between Japan and Taiwan
    • Place of Presentation
      Waseda University
    • Year and Date
      2009-03-09
    • Related Report
      2008 Final Research Report
  • [Presentation] Iwasawa theory and Stickelberger ideals2009

    • Author(s)
      Masato Kurihara
    • Organizer
      Pan Asian Number Theory Conference Pohang
    • Place of Presentation
      Postech
    • Year and Date
      2009-01-10
    • Related Report
      2008 Final Research Report
  • [Presentation] Stickelberger elements and the structure of arithmetic objects2008

    • Author(s)
      Masato Kurihara
    • Organizer
      Iwasawa 2008
    • Place of Presentation
      Irsee, Germany
    • Year and Date
      2008-07-01
    • Related Report
      2008 Annual Research Report 2008 Final Research Report
  • [Presentation] 岩澤理論における行列式表示2008

    • Author(s)
      栗原将人
    • Organizer
      ゼータ関数の行列式表示とその応用
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-03-27
    • Related Report
      2008 Final Research Report 2007 Annual Research Report
  • [Presentation] Several elements related to zeta values2007

    • Author(s)
      Masato Kurihara
    • Organizer
      UK-Japan Winter School 2007 on Number Theory
    • Place of Presentation
      Cambridge University, England
    • Year and Date
      2007-01-07
    • Related Report
      2008 Final Research Report
  • [Presentation] p進ゼータ関数とその数論的応用2006

    • Author(s)
      栗原将人
    • Organizer
      第51回代数学シンポジウム
    • Place of Presentation
      東京大学
    • Year and Date
      2006-08-06
    • Related Report
      2008 Final Research Report
  • [Presentation] Two p-adic L-functions and rational points on elliptic curves with supersingular reduction2006

    • Author(s)
      Masato Kurihara
    • Organizer
      Geometrische Strukturen in der Mathematik, 5th Symposium of the SFB
    • Place of Presentation
      Muenster University
    • Year and Date
      2006-06-08
    • Related Report
      2008 Final Research Report
  • [Presentation] 超特異還元を持つ楕円曲線の p 進 L 関数と有理点2006

    • Author(s)
      栗原将人
    • Organizer
      第11回早稲田大学整数論研究集会
    • Year and Date
      2006-03-15
    • Related Report
      2008 Final Research Report
  • [Presentation] p-adic L-Functions and Rational Points of Elliptic Curves with Supersingular Reduction2006

    • Author(s)
      Masato Kurihara
    • Organizer
      Conference on L-functions
    • Place of Presentation
      Kyushu University
    • Year and Date
      2006-02-22
    • Related Report
      2008 Final Research Report
  • [Presentation] Iwasawa theory and several elements in Galois cohomology2005

    • Author(s)
      Masato Kurihara
    • Organizer
      Open Questions and Recent Developments in Iwasawa Theory in honor of Ralph Greenberg's 60th Birthday
    • Place of Presentation
      Boston University
    • Year and Date
      2005-06-17
    • Related Report
      2008 Final Research Report

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

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