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Zeta functions of prehomogeneous vector spaces

Research Project

Project/Area Number 20540003
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

YUKIE Akihiko  東北大学, 大学院・理学研究科, 教授 (20312548)

Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2008: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywords整数論 / 概均質ベクトル空間 / ゼータ関数 / 密度定理 / 2次形式 / 密度定
Research Abstract

One of the purposes of this investigation was to publish results Obetained before. Two of the preprints finished just prior to this investigation have appeared. The third one is in the process of revision. During the course of finishing this work, I discovered the possibility of extending the notion of the Jordan decomposition and another purpose was to pursue this possibility. Even though I have not finished a preprint, it is progressing and I expect to have a preprint in the near future.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (12 results)

All 2011 2010 2009 2008

All Journal Article (4 results) (of which Peer Reviewed: 4 results) Presentation (3 results) Book (5 results)

  • [Journal Article] On the density of unnormalized Tamagawa Numbers of orthogonal groups II.2009

    • Author(s)
      N. Hayasaka and A. Yukie
    • Journal Title

      Amer. J. Math

      Volume: 131(3) Pages: 683-730

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the density of unnormalized Tamagawa numbers of orthogonal groups II2009

    • Author(s)
      N.Hasyasaka, A.Yukie
    • Journal Title

      Amer.J.Math. 131

      Pages: 683-730

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the density of unnormalized Tamagawa Numbers of orthogonal groups I.2008

    • Author(s)
      N. Hayasaka and A. Yukie
    • Journal Title

      Publ. Res. Inst. Math. Sci.

      Volume: 44(2) Pages: 545-608

    • NAID

      110006648231

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the density of unnormalized Tamagawa numbers of orthogonal groups I2008

    • Author(s)
      N. Hasyasaka and A. Yukie
    • Journal Title

      Publ. Res. Inst. Math. Sci 44

      Pages: 545-607

    • NAID

      110006648231

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] Prehomogeneous vector spaces and number theory2009

    • Author(s)
      雪江明彦
    • Organizer
      東北復旦代数幾何合同シンポジウム
    • Place of Presentation
      東北大学
    • Year and Date
      2009-11-24
    • Related Report
      2010 Final Research Report
  • [Presentation] 概均質ベクトル空間と整数論2009

    • Author(s)
      雪江明彦
    • Organizer
      日本数学会代数学賞受賞記念特別講演
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-28
    • Related Report
      2010 Final Research Report
  • [Presentation] 概均質ベクトル空間と整数論2008

    • Author(s)
      雪江明彦
    • Organizer
      日本数学会2009年度春季総合分科会代数学賞受賞特別講演
    • Place of Presentation
      東京大学
    • Year and Date
      2008-03-28
    • Related Report
      2008 Annual Research Report
  • [Book] 代数学3代数学のひろがり2011

    • Author(s)
      雪江明彦
    • Total Pages
      432
    • Publisher
      日本評論社
    • Related Report
      2010 Final Research Report
  • [Book] 代数学3代数学の広がり2011

    • Author(s)
      雪江明彦
    • Total Pages
      432
    • Publisher
      日本評論社
    • Related Report
      2010 Annual Research Report
  • [Book] 代数学1群論入門2010

    • Author(s)
      雪江明彦
    • Total Pages
      158
    • Publisher
      日本評論社
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Book] 代数学2環と体とガロア理論2010

    • Author(s)
      雪江明彦
    • Total Pages
      300
    • Publisher
      日本評論社
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Book] 概説微分積分学2008

    • Author(s)
      雪江明彦
    • Total Pages
      257
    • Publisher
      培風館
    • Related Report
      2008 Annual Research Report

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Published: 2008-04-01   Modified: 2016-04-21  

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