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Research on Eisenstein series

Research Project

Project/Area Number 14540013
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 Professor, 大学院・理工学研究科, 助教授 (90166033)

Co-Investigator(Kenkyū-buntansha) TSUJI Hajime  Sophia University, Faculty of Science and Engineering, Professor, 理工学部, 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, Associate Professor, 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 Professor, 大学院・理工学研究科, 助教授 (30251599)
Project Period (FY) 2002 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥2,900,000 (Direct Cost: ¥2,900,000)
Fiscal Year 2003: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 2002: ¥1,500,000 (Direct Cost: ¥1,500,000)
KeywordsEisenstein series / Automorphic forms / Discerete groups
Research Abstract

Mizumoto found a new type of series associated to 2n number of elliptic modular forms. This series involves a new special function expressed as an integral of products of modified Bessel functions, and has analytic continuation and functional equation. Such series have not been investigated so far, and they deserve careful study.
Kurokawa constructed and studied multi-trigonomotric functions. Further he studied q-analogues of multi-trigonometric functions, absolute tensor products, absolute differentiation, and spectra of categories.
Shiga investigated the behavior of the solutions of the first boundary value problem (Dirichlet problem) for continuous functions on boundaries of bordered Riemann surfaces ; he showed real analyticity of the solutions with respect to the parameters.

Report

(3 results)
  • 2003 Annual Research Report   Final Research Report Summary
  • 2002 Annual Research Report
  • Research Products

    (24 results)

All Other

All Publications (24 results)

  • [Publications] Mizumoto, S.: "Certain series attached to an even number of elliptic modular forms"Journal of Number Theory. 105. 134-149 (2004)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Kurokawa, N., Wakayama, M.: "A note on spectral zeta functions of quantum groups"International J.Mathematics. 15. 1-10 (2004)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Kurokawa, N., Wakayama, M.: "Absolute tensor products"International Math.Research Noices. 5. 249-260 (2004)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Shiga, H.: "On a distance defined by the length spectrum on Teichmueller space"Ann.Acad.Sci.Fenn.. 28. 315-326 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Schumacher, G., Tsuji, H.: "Quasiprojectivity of moduli space of polarized varieties"Annals of Math.. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Mizumoto, S.: "Certain series attached to an even number of elliptic modular forms"Journal of Number Theory. vol.105. 134-149 (2004)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Kurokawa, N.: "Wakayama, M.A note on spectral zeta functions of quantum groups"International J.Math.. vol.15. 1-10 (2004)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Kurokawa, N.: "Wakayama, Absolute tensor products"International Math.Research Noices. vol.5. 249-260 (2004)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Kurokawa, N.: "Wakayama, Analyticity of plurilogrithmic Euler products"Rendiconti del Circolo Matematico di Palermo. vol.52. 382-388 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Shiga, H.: "On a distance defined by the length spectrum on Teichmueller space"Ann.Acad.Sci.Fenn.. vol.28. 315-326 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Schumacher, G., Tsuji, H: "Quasiprojectivity of moduli space of polarized varieties"Ann.of Math.. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Mizumoto, S.: "Certain series attached to an even number of elliptic modular forms"Journal of Number Theory. 105,no.1. 134-149 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] Kurokawa, N., Wakayama, M.: "A note on spectral zeta functions of quantum groups"International J.Mathematics. 15. 1-10 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] Kurokawa, N., Wakayama, M.: "Absolute tensor products"International Math.Research Noices. 5. 249-260 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] Shiga, H.: "On a distance defined by the length spectrum on Teichmueller space"Ann.Acad.Sci.Fenn.. 28. 315-326 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Schumacher, G., Tsuji, H.: "Quasiprojectivity of moduli space of polarized varieties"Annals of Math.. (to appear).

    • Related Report
      2003 Annual Research Report
  • [Publications] Fujisawa, T., Nakayama, C.: "Mixed Hodge structures on log deformations"Rendiconti del Seminario Matematico di Padova. 110. 221-268 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Kurokawa, N., Wakayama, M.: "Zeta extensions"Proc.Japan Acad.. 78,no.7. 126-130 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Kurokawa, N., Eva-Marie, M.-S., Ochiai, H., Wakayama, M.: "Kronecker's Jugendtraum and ring sine functions"J. Ramanujan Math. Soc.. 17,no.3. 211-220 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Kurokawa, N., Ochiai, H., Wakayama, M.: "Multiple trigonometry and zeta functions"J. Ramanujan Math. Soc.. 17,no.2. 101-113 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Tsuji, H.: "Deformation invariance of plurigenera"Nagoya Math. J.. 166. 117-134 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Tsuji, H.(with G.Schumacher): "Quasiprojectivity of Moduli Spaces of Polarized Varieties"Annals of Mathematics. (to appear).

    • Related Report
      2002 Annual Research Report
  • [Publications] Tsuji, H.: "Subadjunction Theorem"Proceedings of Oka 100. (to appear).

    • Related Report
      2002 Annual Research Report
  • [Publications] Shiga, H.: "Dirichlet solutions on bordered Riemann surfaces and quasiconformal mappings"J. d'Analyse. Math.. (to appear).

    • Related Report
      2002 Annual Research Report

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Published: 2002-04-01   Modified: 2016-04-21  

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