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On correlation among some properties of arithmetic zeta functions

Research Project

Project/Area Number 25800031
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Algebra
Research InstitutionTokyo Denki University

Principal Investigator

Mishou Hidehiko  東京電機大学, 情報環境学部, 准教授 (10435456)

Project Period (FY) 2013-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywordsゼータ関数 / 数論的ゼータ関数 / 普遍性 / 値分布 / 零点分布
Outline of Final Research Achievements

On Theme 1 "Steuding Conjecture", I obtained the joint universality theorem for a pair of zeta functions with real coefficients and the joint universality theorem for a set of the Riemann zeta function and two automorphic L-functions.
On Theme 2 "Value distribution of the Riemann zeta function z(s) with respect to the imaginary part of zeros", I showed that for a positive number d less than 1, the universality property holds for z(s+idg) as g varies, where g denotes the imaginary part of a complex zero of z(s).
On Theme 3 "Joint universality for zeta functions with respect to arithmetic parameters", I obtained that the joint universality theorem for Dirichlet L-functions in the character aspect and the joint universality theorem for quadratic L-functions in the real character aspect (joint work with Hirofumi Nagoshi (Gunma University)).

Report

(4 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (6 results)

All 2014 2013

All Journal Article (2 results) (of which Peer Reviewed: 2 results) Presentation (4 results) (of which Invited: 1 results)

  • [Journal Article] Joint universality theorems for pairs of automorphic zeta functions2014

    • Author(s)
      Hidehiko Mishou
    • Journal Title

      Mathematische Zeitschrift

      Volume: 印刷中

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Functional distribution for a collection of Lerch zeta functions2014

    • Author(s)
      Hidehiko Mishou
    • Journal Title

      Journal of Mathematical Society of Japan

      Volume: 印刷中

    • NAID

      130004705995

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Presentation] ゼータ関数の普遍性の概要2014

    • Author(s)
      見正秀彦
    • Organizer
      日本数学会 2014年秋季総合分科会 代数学分科会 特別講演
    • Place of Presentation
      広島大学(広島県東広島市)
    • Year and Date
      2014-09-25
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] 実指標 Dirichlet L 関数間の同時 d - 普遍性と類数たちの多次元稠密性2014

    • Author(s)
      見正秀彦,名越弘文(発表者は見正)
    • Organizer
      日本数学会 2014年秋季総合分科会 代数学分科会 一般講演
    • Place of Presentation
      広島大学(広島県東広島市)
    • Year and Date
      2014-09-25
    • Related Report
      2014 Research-status Report
  • [Presentation] A new method to prove joint universality for zeta functions2013

    • Author(s)
      Hidehiko Mishou
    • Organizer
      Palanga Conference in Combinatroics and Number Theory
    • Place of Presentation
      Palanga, Lithuania
    • Related Report
      2013 Research-status Report
  • [Presentation] 同時普遍性を持つ任意個数の保型L関数たちの例2013

    • Author(s)
      名越弘文(群馬大学)(講演者)、見正秀彦
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      愛媛大学
    • Related Report
      2013 Research-status Report

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Published: 2014-07-25   Modified: 2019-07-29  

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