• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Stadies on Andytic Priepeitied of autoinoiptic L-functions

Research Project

Project/Area Number 16340002
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionNagoya University

Principal Investigator

MATSUMOTO Koji  Nagoya University, Grad. Sch. Math, Prof (60192754)

Co-Investigator(Kenkyū-buntansha) KONDO Shigeyuki  Nagaya Univ, Grad. Sch. Math, Prof (50186847)
KANEMITU Shigeru  Kinki Univ, Dept. Eng, Prof. (60117091)
KANEKO Masahiko  Kyoetsu Univ, Grad. Sch. Math, Prof (70202017)
EGAMI Shigeki  Tayama Univ, Fac. Eng, Assit. Prof (60168771)
KOJIMA Hisashi  Saitama Univ, Fac. Sci, Prof (90146118)
谷川 好男  名古屋大学, 大学院多元数理科学研究科, 助教授 (50109261)
古庄 英和  名古屋大学, 大学院多元数理科学研究科, 助手 (60377976)
坂内 健一  名古屋大学, 大学院・多元数理科学研究科, 助手 (90343201)
Project Period (FY) 2004 – 2007
Project Status Completed (Fiscal Year 2007)
Budget Amount *help
¥17,520,000 (Direct Cost: ¥16,200,000、Indirect Cost: ¥1,320,000)
Fiscal Year 2007: ¥5,720,000 (Direct Cost: ¥4,400,000、Indirect Cost: ¥1,320,000)
Fiscal Year 2006: ¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2005: ¥4,400,000 (Direct Cost: ¥4,400,000)
Fiscal Year 2004: ¥3,800,000 (Direct Cost: ¥3,800,000)
Keywordsautomcrphic L-function / automacrphic form / automcrphic L-fiuiction / Ikeda lifting / mean-valat fheoreul / multiple zeta-fanction / multiple L-function / 平均値定理 / Wittenゼータ関数 / ルート系 / 半単純Lie環 / 関数関係式 / Weyl群 / 関数等式 / Siegelモジュラー形式 / 二乗平均値定理 / スタンダードL関数 / Mellin-Barnes積分 / 標準L関数 / Riemannゼータ関数
Research Abstract

First, we have developed the theory of modular relations and have given a unified treatment of functional equations, approximate functional equations and asymptotic expansions in view of modular relations. From this viewpoint, we gave a modular-theoretic proof of asymptotic expansion formulas of Katsurada and Matsumoto on Dirichlet L-functions and Hurwitz zeta-functions. Secondly, on Ikeda liftings of Siegel modular forms, we have shown-a part of Kohnen's conjecture on the image space of Ikeda liftings. We have proved rather sharp asymptotic formula for the mean square of standard L-functions attached to modular forms which are Ikeda lifts. In particular, applying a large value lemma, we almost determined the true order of the mean square in some cases. As for the theory of multiple zeta-functions, we have developed the study of double shuffle relations of multiple zeta values, and have clarified their arithmetic structure. Also we discovered that the functional relations among multiple zeta-functions can be explained by the symmetry of Weyl groups of underlying Lie algebras. Moreover we have found that the recursive structure of the family of multiple zeta-functions can be described in terms of Dynkin diagrams.

Report

(5 results)
  • 2007 Annual Research Report   Final Research Report Summary
  • 2006 Annual Research Report
  • 2005 Annual Research Report
  • 2004 Annual Research Report
  • Research Products

    (33 results)

All 2007 2006 2005 2004 Other

All Journal Article (27 results) (of which Peer Reviewed: 6 results) Presentation (5 results) Book (1 results)

  • [Journal Article] Canvolutions of the von Mangoldt function and related Dirichlet series2007

    • Author(s)
      S. Egami, K. Matsumoto
    • Journal Title

      in "Number Theory", Series on Number Theory and its Appl. 2

      Pages: 1-23

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On ordinary primes for modular forms and the thera operator2007

    • Author(s)
      M. Chida, M. Kaneko
    • Journal Title

      Proc. Amer. Math. Soc. 135

      Pages: 1001-1005

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Regularization and generalized double shuffle relation for p-adic multiple zeta values2007

    • Author(s)
      H. Furusho, A. Jafari
    • Journal Title

      Compositio Math. 143

      Pages: 1089-1107

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On Wiffen multiple zeta-functions associated with semisimple lie algebras I2006

    • Author(s)
      K. Matsumoto, H. Tsumura
    • Journal Title

      Ann. Inst. Fourier 56

      Pages: 1457-1504

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] On Wuttcm Multiple Zeta-fimctions arectiated with aeuiciniple Lie Algelnas I2006

    • Author(s)
      K. Mateumoto, H. Tsumcura
    • Journal Title

      Ann. Inet 56

      Pages: 1457-1504

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Some number-tlunctic application of a genetal modulan naltim2006

    • Author(s)
      S. Kanenicteu, Y. Tauigaut, H. Tsuleada
    • Journal Title

      Intem. J. Number Thecny 2

      Pages: 599-615

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] On the mean square of standard L-funcrions attached to Ikada lifts2006

    • Author(s)
      K.Matsumoto, A.Sankaranarayanam
    • Journal Title

      Math. Z. 253

      Pages: 607-622

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Generalized multiple Dirithlet Series and generalized multife polylogarithms2006

    • Author(s)
      K.Matsumoto, H.Tsumura
    • Journal Title

      AcTa Arith. 124

      Pages: 139-158

    • Related Report
      2006 Annual Research Report
  • [Journal Article] On witten multiple zeta-fuuctions associated with semisimple Lie algebras I2006

    • Author(s)
      K.Matsumoto, H.Tsumura
    • Journal Title

      Ann. Inst. Fourier 56

      Pages: 1457-1504

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Joint value-distribution theorems on Lerch zeta-functions II2006

    • Author(s)
      A.Laurincikas, K.Matsumoto
    • Journal Title

      Liet. Mat. Rink. 46

      Pages: 332-350

    • Related Report
      2006 Annual Research Report
  • [Journal Article] On the speed of convergence to limit distributions for Hecke L-functions assoc with ideal class characters2006

    • Author(s)
      K.Matsumoto
    • Journal Title

      Analysis 26

      Pages: 313-321

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Some aspects of the modular relation2006

    • Author(s)
      S.Kanemitsu, Y.Tanigawa, H.Tsukada, M.Yoshimoto
    • Journal Title

      "Number Theory : Tradition and Modernization", Dev. Math. 15

      Pages: 103-118

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Liftings and mean value theorems for automorphic L-fimctions2005

    • Author(s)
      K. Matsumoto
    • Journal Title

      Proc. London Math. Soc. (3)90

      Pages: 297-320

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Liftings and mean valece themcas for automarphic L-fancrions2005

    • Author(s)
      K. Mataumoto
    • Journal Title

      Proc. Lendon Mate. Soc (3) 90

      Pages: 297-320

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Liftings and mean value theorems for automorphic L-functions2005

    • Author(s)
      K.Matsumoto
    • Journal Title

      Proc.London Math.Soc. (3)90

      Pages: 297-320

    • Related Report
      2005 Annual Research Report 2004 Annual Research Report
  • [Journal Article] The analytic continuation and the asymptotic behaviour of certain multiple zeta-functions III2005

    • Author(s)
      K.Matsumoto
    • Journal Title

      Comment.Math.Univ.St.Pauli 54

      Pages: 163-186

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Discrete universality of L-functions for new forms2005

    • Author(s)
      A.Laurincikas, K.Matsumoto, J.Steuding
    • Journal Title

      Math.Notes 78

      Pages: 551-558

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Convolution of Riemann zeta values2005

    • Author(s)
      S.Kanemitsu, Y.Tanigawa, M.Yoshimoto
    • Journal Title

      J.Math.Soc.Japan 57

      Pages: 1167-1177

    • Related Report
      2005 Annual Research Report
  • [Journal Article] P-adic multiple zeta values I2004

    • Author(s)
      H. Furusho
    • Journal Title

      Invent. Math. 155

      Pages: 253-286

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] P-adic muiltipe zte values I2004

    • Author(s)
      H. Furusho
    • Journal Title

      Invent. Math 155

      Pages: 253-286

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Functional equations for double zeta-functions2004

    • Author(s)
      K.Matsumoto
    • Journal Title

      Math.Proc.Cambridge Phil.Soc. 136

      Pages: 1-7

    • Related Report
      2004 Annual Research Report
  • [Journal Article] The joint universality of twisted automorphic L-functions2004

    • Author(s)
      A.Laurincikas, K.Matsumoto
    • Journal Title

      J.Math.Soc.Japan 56

      Pages: 923-939

    • Related Report
      2004 Annual Research Report
  • [Journal Article] On the mean square of the product of ζ(s) and a Dirichlet polynomial2004

    • Author(s)
      K.Matsumoto
    • Journal Title

      Comment Math.Univ.St.Pauli 53

      Pages: 1-21

    • Related Report
      2004 Annual Research Report
  • [Journal Article] P-adic multiple zeta values I, p-adic multiple polylogarithms and the p-adic KZ-equation2004

    • Author(s)
      H.Furusho
    • Journal Title

      Invent.Math. 155

      Pages: 253-286

    • Related Report
      2004 Annual Research Report
  • [Journal Article] On the discrete mean square of Dirichlet L-functions at 12004

    • Author(s)
      S.Kanemitsu, Y.Tanigawa, M.Yoshimoto, W.Zhang
    • Journal Title

      Math.Z. 248

      Pages: 21-44

    • Related Report
      2004 Annual Research Report
  • [Journal Article] On the mean square of standard L-functions attached to Ikeda lifts

    • Author(s)
      K.Matsumoto, A.Sankaranarayanan
    • Journal Title

      Math.Z. (to appear)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] On Witten multiple zeta-functions associated with semisimple Lie algebras I

    • Author(s)
      K.Matsumoto, H.Tsumura
    • Journal Title

      Ann.Inst.Fourier (to appear)

    • Related Report
      2005 Annual Research Report
  • [Presentation] On the value distribution of Dedekind zeta functions2007

    • Author(s)
      松本 耕二
    • Organizer
      Analyse Harmonique et Theorie Anolytigue
    • Place of Presentation
      リール第一大学,リール(仏)
    • Year and Date
      2007-11-12
    • Related Report
      2007 Annual Research Report
  • [Presentation] The moduli of plane quantics and Brdunds Produots2007

    • Author(s)
      S. Kondo
    • Organizer
      "Modulav Forms and Moduli Spaces", Fsetuinal didicated to booth, Brithday of L. Eulen, St.-Piteneling
    • Place of Presentation
      Rueeia
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Mean aguane valcus of atandand L-functions attadied to Ikeda lifts2006

    • Author(s)
      K. Matsumato
    • Organizer
      Number Thary Sencican, Univ de Bardeaux 1
    • Place of Presentation
      Bordeaux, France
    • Year and Date
      2006-11-17
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 多重ゼータ関数の解析的理論とその応用2005

    • Author(s)
      松本 耕二
    • Organizer
      日本数学会年会
    • Place of Presentation
      日本大学
    • Year and Date
      2005-03-29
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] The analytic tlaory of nudltiple zeta-functions and application2005

    • Author(s)
      K. Mateumete
    • Organizer
      Math. Soe. Japan
    • Place of Presentation
      NIhon, Univ. Tokyo
    • Year and Date
      2005-03-29
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Book] リーマンのゼータ関数2005

    • Author(s)
      松本 耕二
    • Total Pages
      218
    • Publisher
      朝倉書店
    • Related Report
      2005 Annual Research Report

URL: 

Published: 2004-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi