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1999 Fiscal Year Final Research Report Summary

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
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.

  • Research Products

    (17 results)

All Other

All Publications (17 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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [Publications] Hiroshige Shiga: "Complex Analysis II (Japanese)"Baifukan : Tokyo. (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [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

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Published: 2001-10-23  

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