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Geometric Study of Complex Analysis

Research Project

Project/Area Number 09440054
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field 解析学
Research InstitutionKanazawa University

Principal Investigator

FUJIMOTO Hirotaka  Kanazawa University, Faculty of Science, Professor, 理学部, 教授 (60023595)

Co-Investigator(Kenkyū-buntansha) NOGUCHI Junjiro  Tokyo University, Graduate School of Mathematical Science, Professor, 数理科学研究科, 教授 (20033920)
IWASE Junichi  Kanazawa University, Faculty of Science, Assistant, 理学部, 助手 (70183746)
ISHIMOTO Hiroyasu  Kanazawa University, Faculty of Science, Professor, 理学部, 教授 (90019472)
TOMARI Masataka  Kanazawa University, Graduate School of Natural Science and Technology, Associat, 自然科学研究科, 助教授 (60183878)
KODAMA Akio  Kanazawa University, Faculty of Science, Professor, 理学部, 教授 (20111320)
高信 敏  金沢大学, 理学部, 助教授 (40197124)
森下 昌紀  金沢大学, 理学部, 助教授 (40242515)
菅野 孝史  金沢大学, 理学部, 教授 (30183841)
Project Period (FY) 1997 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 1998: ¥3,400,000 (Direct Cost: ¥3,400,000)
Keywordsvalue distribution theory / uniqueness theorems / automorphic form / algebraic group / adele geometry / isolated singularity / automorphsm group / CR-invariant / 代数的退化定理 / 一意性問題 / 複素線型微分方程式 / ラングの予想 / 正則自己同型群 / アデール幾何学 / ポアンカレー予想 / 正則曲線の一意的定理 / ア-デル幾何 / CR-不変計量
Research Abstract

Head investigator Fujimoto studied value-distribution-theoretic properties of meromorphic maps of C^n into P^N(C) and gave some new results as their applications.
He showed that, for 3N +1 hyperplanes H_j's in P^N(C) located in general position, there exists at most two meromorphic maps f of C^n into P^N(C) such that the inverse images f^<-1>(H_j)'s, which are counted with multiplicities truncated by two, coincide with given divisors D_j's. He also proved that, for 2N +2 hyperplanes H_j, in P^N(C) located in general position, there is some positive integer l_0 such that, if two meromorphic maps f and g of C^n into P_N(C) have the same inverse images counted with multiplicities truncated by l_0 for each H_j, then f and g are algebraically degenerate.
He also studied uniqueness range sets for meromorphic functions on C, namely, sets S with the property that the condition f^<-1>(S) = g^<-1>(S), counted f, g on C.For a finite set S = {a_1, a_2, ・・・, a_q}, he considers the polynomial P(w) : = (w - a_1)(w - a_2)・・・(w - a_q) and assumes that the derivative P(w) has k distinct zeros d_1, d_2, ・・・, d_h. He showed that, if k <greater than or equal> 4, q > 2k + 6, P(d_l) * P(d_m) for l * m and SIGMA_l P(d_l) * 0, then S is a uniqueness range set. He also gives some other sufficient conditions for a finite set to be a uniqueness range set.

Report

(3 results)
  • 1998 Annual Research Report   Final Research Report Summary
  • 1997 Annual Research Report
  • Research Products

    (47 results)

All Other

All Publications (47 results)

  • [Publications] Hirotaka Fujimoto: "Uniqueness problem with truncated multiplicities in value distribution theory" Nagoya Math. J.152. 131-152 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Fujimoto: "Uniqueness problem with truncated multiplicities in value distribution theory II" Nagoya Math. J.未定. (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K.Ishizaki K Tohge: "On the complex oscillation of some linear differential equations" J.of Math. Analysis and Appl.206. 503-517 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K.Ishizuki K.Tohge: "Hypentrans cendency of meronayhic solutions of a functional ecascation" Report.of Researhes of NIT. 27. 479-484 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] N.Kobayakawa M.Ishimura: "Homototopy classification of Sulbiciently cnnected manifolds" Sci.Rep.Kanazawa Univ.43. 1-30 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] A.Kodama: "A Characterization of certain weaboly pseudoconvex domains" Tohoku Math. J.51. (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Morishita: "On a family of subgroups of the Teichmuller modular group of genus two obtained from the Jones representation" J.Math.Sci.Univ.Tokyo. 4. 402-415 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Morishita and T.Watanabe: "On S-Hardy-Little wood hauogene ons sha as" Inter national Journal of Mathematics. 9. 723-757 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] A.Murase and T.Sugano: "On standard L-function attached to autonamorphic fours an delinite or lhogonal groups" Nagoya Math. J.152. 1-40 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] J.Noguchi: "Neutral in the cartam theory over function fields and a Diophantine equation" J.veine angew. Math. 489. 61-83 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] J.Noguchi: "On hdonaybic curves in semi-Abelian varieties" Math. Z.,. 228. 713-721 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] J.Noguchi: "Value distribution theory of holomorphic 〓" Cnitemp. Math.222. 109-129 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] J.Noguchi: "Introduction to Complex analysis" Ame.Math.Soc.,Rhode Island, 250 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Fujimoto: "Uniqueness probblem with truncated multiplicities in value distribution theory" Nagoya Math.J.152. 1-21 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Fujimoto: "Uniqueness probblem with truncated multiplicities in value distribution theory, II" Nagoya Math.J..(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K.Ishizaki and Tohge: "On the complex oscillation of some linear differential equations" Journal of Mathemathematical Analysis and Applications. 206. 503-517 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K.Ishizaki and Tohge: "Hypertranscendency of meromorphic solutions of a functional equation" Report of researches of Nippon Institute of Technology. 27. 479-484 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] N.Kobayakawa and H.Ishimoto: "Homotopy classification of suffi-ciently connected manifolds" Sci.Rep.Kanazawa Univ.43. 1-30 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] A.Kodama: "An application of Webster's CR-invariant metric to a characterization of generalized complex ellipsoids" Proc.of the Fifth Intern. Colloquium on Complex Analysis, Peking University. 173-176 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] A.Kodama: "A characterization of certain weakly pseudoconvex do-mains" Tohoku Math.J.51(to appear. (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Morishita: "On a fimily of subgroups of the Teichmuller modular group of genus tow obtained from the Jones representation" J.Math.Sci.Univ.Tokkyo. 4. 402-415 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Morishita and T.Watanabe: "On S-Hardy Littlewood homogeneous spaces" Infern.J.Math.9. 723-757 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Morishita and T.Watanabe: "Adewle geometry of numbers" Calss Field Theory-its Centenary and Prospect (ed.by K.Miyake), The Advanced Studies in Pure Mathematics Series.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] A.Murase and T.Sugano: "On standard L-functions attached to au-tomorphic forms on definite orthogonal groups" Nagoya Math.J.152. 1-40 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] J.Noguchi: "Nevanlinna-Cartan theory over function fields and a Dio-phantine equation" J.reine angew.Math.489. 61-83 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] J.Noguchi: "Introduction to complex analysis" MMONO Amer.Math.Soc., Rhode Island. 168. xii+250 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] J.Noguchi: "Recent topics in the theory of holomorphic curves, Proc.Internat" Workshop on the value distribution theory and its applica-tions, Ed.C.-C.Yang, Grodon and Breach Scie.Publ.Amsterdam. 317-331 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] J.Noguchi: "On holomorphic curves in semi-Abelian varieties" Math.Z.228. 713-721 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] J.Noguchi: "Value distribution theory of holomorphic mappings" Con-temp.Math.222. 109-129 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Morishita T.Watanabe: "On S-Hardy-Littlewood homogeneous spaces" International Journal of Mathematics. 9-6. 723-757 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] K.Ishizaki and K.Tohge: "On the complex oscinllation of some linear differential equations" J.Math.Analysis and Appl.206-2. 503-517 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] K.Ishizaki and K.Thoge: "Hypertranscendency of meronorphic solutions of a feendial equations" Report of researches of Nippon-Institute of Technology. 27. 479-484 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] J.Noguchi: "Nevanlinna-Carton theory over function fields and a Diophantine equation" J.reine angew.Math.487. 61-83 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] J.Noguchi: "On holomorphic curves in semi-Abelian varieties" Mathematische Zeitsschift. 228. 713-721 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] J.Noguchi: "Value distribution theory of holomorphic mappings" Contemp.Math.222. 109-129 (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] Hirotaka Fujimoto: "Uniqueness problem with trancated multiplicities in value distribution theory" Nagoya Mathematical Journal. 152. 131-152 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Hirotaka Fujimoto: "Uniqueness with trancated multiplicities in value distribution theory II" Nagoya Mathematical Jounal. (未定). (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] Akio Kodama: "An application of Webster's CR-invariant metric to a characterization of generalized complex ellipsoids" Proc.of the Fifth Intern.Collogium on confpex Andys.173-176 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] Akio Kodama: "A characterization of certain wealdly peenlocorrex domains" To^^<^>hoku Math.J.,. 51. (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] A.Murase and T.Sugano: "On standard L-functions attached to automophic forms on deginite orthgonal groups" Nagoya Mathematical Jounal. 152. 1-40 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] M.Morishita: "On a family of subgroups of the Teichmuller Modular grop of genus two obtained from the Jones Representation" J.Math.Sci.Univ.Tokyo. 4. 403-415 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] Hirotaka Fujimoto: "Uniqueness problem with truncated multilicities in value distribution theory" Nagoya Mathematical Journal. (未定). (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] Masanori Morishita: "On a fornity of subgroups of the Teichmuller modular group of gene two obtained from the Johns representation" J.of Math.Sci.Univ.of Tokyo. 4. 403-415 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Masanori Morishita: "On S-Hardy-Littlewood homogeneons spaces" International J.Math.(未定). (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] Takashi Sugeno A.Murase: "On standard L-functions attached to automorphic forms on definite arthogonal groups" Nagoya Math.J.(未定). (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] T.Ichinose S.Takanobu: "Estimate of the difference between the Kac operator and Schrodinge semigroup" Comm.Math.Phys.186. 167-197 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] S.Takanobu: "On the error estimate of the integral kernel for the Trotter product of mula for Schrodinger operators" Ann.Prof.(未定).

    • Related Report
      1997 Annual Research Report

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

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