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Graded rings of modular forms in higher genera and algebraic combinatorics

Research Project

Project/Area Number 25400014
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionKanazawa University (2014-2015)
Kochi University (2013)

Principal Investigator

Oura Manabu  金沢大学, 数物科学系, 教授 (50343380)

Project Period (FY) 2013-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
KeywordsE-多項式 / 符号 / モジュラー形式 / 中心化環 / テータ / 格子 / Eisenstein級数 / 複素球面上の点集合 / Barnes-Wall格子 / 不変式論
Outline of Final Research Achievements

We have work in the boundary between the theory of modular forms and that of algebraic combinatorics. With Masashi Kosusa, we determined the structures of the centralizer rings of the tensor representation of the group associated to Type II binary codes. With Togo Motomura, we determined the generators of the garded ring of E-polynomials associated to Type II Z4-codes. With Michio Ozeki, we studied the theta series of five extremal Type II lattices of rank 85 and showed that they are distinct in genus four.

Report

(4 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (4 results)

All 2015 2014 Other

All Presentation (2 results) Remarks (1 results) Funded Workshop (1 results)

  • [Presentation] Theta series of even nimodular extremal lattices2015

    • Author(s)
      大浦 学
    • Organizer
      2015 早稲田整数論研究集会
    • Place of Presentation
      早稲田大学
    • Year and Date
      2015-03-20
    • Related Report
      2014 Research-status Report
  • [Presentation] E-多項式について2014

    • Author(s)
      大浦学
    • Organizer
      有限群とその表現、頂点作用素代数、代数的組合せ論の研究
    • Place of Presentation
      京都大学数理研
    • Related Report
      2013 Research-status Report
  • [Remarks]

    • URL

      http://sphere.s.kanazawa-u.ac.jp

    • Related Report
      2014 Research-status Report
  • [Funded Workshop] RIMS研究集会「計算代数システムによる新しい数学の開拓と進展」2015

    • Place of Presentation
      京都大学
    • Year and Date
      2015-09-30
    • Related Report
      2015 Annual Research Report

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Published: 2014-07-25   Modified: 2019-07-29  

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