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Research on nearly holomorphic modular forms

Research Project

Project/Area Number 10640010
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionTokyo Institute of Technology

Principal Investigator

MIZUMOTO Shin-ichiro  TOKYO INSTITUTE OF TECHNOLOGY, Graduate School of Science and Engineering, Associate Prof., 大学院・理工学研究科, 助教授 (90166033)

Co-Investigator(Kenkyū-buntansha) TSUJI Hajime  TOKYO INSTITUTE OF TECHNOLOGY, Graduate School of Science and Engineering, Associate Prof., 大学院・理工学研究科, 助教授 (30172000)
SHIGA Hiroshige  TOKYO INSTITUTE OF TECHNOLOGY, Graduate School of Science and Engineering, Professor, 大学院・理工学研究科, 教授 (10154189)
KUROKAWA Nobushige  TOKYO INSTITUTE OF TECHNOLOGY, Graduate School of Science and Engineering, Professor, 大学院・理工学研究科, 教授 (70114866)
NAKAYAMA Chikara  TOKYO INSTITUTE OF TECHNOLOGY, Graduate School of Science and Engineering, Research Associate, 大学院・理工学研究科, 助手 (70272664)
HATTORI Toshiaki  TOKYO INSTITUTE OF TECHNOLOGY, Graduate School of Science and Engineering, Associate Prof., 大学院・理工学研究科, 助教授 (30251599)
Project Period (FY) 1998 – 1999
Project Status Completed (Fiscal Year 1999)
Budget Amount *help
¥3,000,000 (Direct Cost: ¥3,000,000)
Fiscal Year 1999: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 1998: ¥1,600,000 (Direct Cost: ¥1,600,000)
KeywordsAtomorphic forms / L-functions / Discrete groups
Research Abstract

Mizumoto studied the central zeros of the Rankin L-functions associated to a pair of holomorphic modular forms for SL(2, Z); he obtained a nonvanishing result for them.
Kurokawa studied the spectra of Laplace operators on categories. He proved its semipositivity and obtained some asymptotic results. The results are expected to have some connection with zeta functions of categories.
Shiga proved analogy between the limit set of Kleininan groups and the Julia set (as a function-theoretic set) in complex dynamical systems. He also studied rigidity and finiteness of holomophic mappings on complex hyperbolic manifolds.
Tsuji studied applications of singular hermitian metrics. In particular, he obtained a satisfactory result on the structure of canonical rings and on the quasi-projectivity of moduli spaces of polarized algebraic varieties.
Hattori studied quasi-isometry invariants of discrete groups. In particular, he investigated uniform lattices in Lie groups.
Nakayama studied log geometry for complex analyic spaces. Using the theory so obtained, he proved the degeneration of l-adic weight spectral sequences over an arbitrary field. He also studied relations between log Hodge structures and log abelian varieties.

Report

(3 results)
  • 1999 Annual Research Report   Final Research Report Summary
  • 1998 Annual Research Report
  • Research Products

    (30 results)

All Other

All Publications (30 results)

  • [Publications] Shin-ichiro Mizumoto: "Certain L-functions at S = 1/2"Acta Arithmetica. 88. 51-66 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H. Shiga and H. Tanigawa: "Projective structures on Riemann Surfaces with holonomies discontinuous"Trans. Amer. Math. Soc.. 351. 813-823 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] K. Kato and C. Nakayama: "Log Betti cohomology, log etale cohomology, and log de Rham cohomology of log schemes over C"Kodai Math. J. 22. 161-186 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] C. Nakayama: "Degeneration of l-adic weight spectral sequences"Amer. J. Math.. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] N. Kurokawa, H. Tanuma and R. Sasaki: "Spectra of categories"Proc, Japan Acad.. 75. 92-95 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] N. Kurokawa and M. Wakayama: "A formula for the multiplicity of principal series in L^2(T/G)"Forum Math..

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H. Tsuji: "Existence and applications of analytic Zariski decompositions"Trends in Math : Birkhauser. - (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 志賀啓成: "複素解析学II"培風館. 181 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 黒川信重(他三名): "ゼータの世界"日本評論社. 158 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Shin-ichiro Mizumoto: "Certain L-functions at s = 1/2"Acta Arithmetica. 88. 51-66 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H. Shiga, H. Tanigawa: "Projective structures on Riemann surfaces with discontinuous holonomies"Trans. Amer. Math. Soc.. 351. 813-823 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] K. Kato and C. Nakayama: "Log Betti cohomology, log etale cohomology, and log de Rham cohomology of log schemes over C"Kodai Math. J.. 22. 161-186 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Chikara Nakayama: "Degeneration of l-adic weight spectral sequences"Amer. J. Math.. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] N. Kurokawa, R. Sasaki and H. Tanuma: "Spectra of categories"Proc. Japan Acad.. 75. 92-95 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Hajime Tsuji: "Existence and applications of analytic Zariski decompositions"Trends in Math : Birkhauser. (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Hiroshige Shiga: "Complex Analysis II (Japanese)"Baifukan : Tokyo. (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Nobushige Kurokawa et al.: "The World of ζ"Nihon Hyoron sha : Tokyo. (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Shinichirou Mizumoto: "Certain L-functions at s=1/2"Acta Arithmetica. 88(no.1). 51-66 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] H.Shiga and H.Tanigawa: "Projective structures on Riemann surfaces with discontinuous holonomies"Trans. Amer. Math. Soc. 351. 813-823 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] K.Kato and C.Nakayama: "Log Bettic cohomology, log etale cohomology. And log de Rham cohomology of log schemes over C"Kodai Math. J. 22. 161-186 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] C.Nakayama: "Degeneration of l-adic weight spectual sequences"Amer.J. Math. (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] N.Kurokawa,R.Sasaki and H.Tamura: "Spectra of categories"Proc. Japan Acad. 75(no.6). 92-95 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] H.Tsuji: "Existence and Applications of Analytic Zariski Decompositions"Trends in Math: Birkhauser. (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 志賀啓成: "複素解析学II"培風館. 181 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 黒川信重(他3名): "ゼータの世界"日本評論社. 158 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Shin-ichiro Mizumoto: "Certain L-functions at s=1/2" Acta Arithmetica. (to appear).

    • Related Report
      1998 Annual Research Report
  • [Publications] 黒川信重: "量子空間とRiemann予想" 日本物理学会誌. 53巻9号. 696-699 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Shiga and H.Tanigawa: "Projective structures on Riemann surfaces with discontinuous holonomies" Trans.Amer.Math.Soc.(to appear).

    • Related Report
      1998 Annual Research Report
  • [Publications] Hajime Tsuji: "Existence and applications of analytic Zariski decomposition" Proc.of 40-th Taniguchi Conference. (to appear).

    • Related Report
      1998 Annual Research Report
  • [Publications] Chikara Nakayama: "A projection formula for log smooth varieties in log etale coho-mology" Preprint series TITECH-MATH 12-97(# 76).

    • Related Report
      1998 Annual Research Report

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Published: 1998-04-01   Modified: 2016-04-21  

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