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Study on the theory of approximation for L-functions

Research Project

Project/Area Number 25400005
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionGunma University

Principal Investigator

Nagoshi Hirofumi  群馬大学, 大学院理工学府, 准教授 (70571165)

Project Period (FY) 2013-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
KeywordsL関数 / 値分布 / 独立性 / セルバーグ直交性 / セルバーグ・クラス / 普遍性定理 / 一般リーマン予想 / ゼータ関数 / 関数的独立性
Outline of Final Research Achievements

We studied the so-called joint universality properties in the theory of value-distribution of L-functions and established several results in the cases of the t-aspect, q-aspect and d-aspect. As a related topic, we also studied zeros of L-functions associated with holomorphic cusp forms for SL(2,Z). Furthermore, we obtained several results on independence of L-functions, by applying Selberg's orthogonality.

Report

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

    (8 results)

All 2016 2015 2014 Other

All Journal Article (2 results) (of which Peer Reviewed: 2 results,  Open Access: 2 results,  Acknowledgement Compliant: 2 results) Presentation (6 results) (of which Int'l Joint Research: 1 results)

  • [Journal Article] Hypertranscendence of L-functions for GL_m (A_Q)2016

    • Author(s)
      Hirofumi Nagoshi
    • Journal Title

      Bulletin of the Australian Mathematical Society

      Volume: 93 Issue: 3 Pages: 388-399

    • DOI

      10.1017/s000497271500129x

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Joint value-distribution of L-functions and discrepancy of Hecke eigenvalues2016

    • Author(s)
      Hirofumi Nagoshi
    • Journal Title

      Lithuanian Mathematical Journal

      Volume: 56

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Presentation] Zeros of the L-function attached to a cusp form and some applications of Selberg's orthogonality2015

    • Author(s)
      Hirofumi Nagoshi
    • Organizer
      Analytic Number Theory and Related Areas
    • Place of Presentation
      京都大学数理解析研究所(京都府・京都市)
    • Year and Date
      2015-11-05
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] The existence of zeros of non-primitive L-functions for SL(2,Z) in the strip 1/2 < Re s < 12015

    • Author(s)
      名越弘文
    • Organizer
      Diophantine Analysis and Related Fields 2015
    • Place of Presentation
      桐生市市民文化会館
    • Year and Date
      2015-03-07
    • Related Report
      2014 Research-status Report
  • [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
    • Organizer
      日本数学会2014年度秋季総合分科会
    • Place of Presentation
      広島大学
    • Year and Date
      2014-09-25
    • Related Report
      2014 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

    • Author(s)
      名越弘文,見正秀彦
    • Organizer
      日本数学会2013年度秋季総合分科会
    • Place of Presentation
      愛媛大学
    • Related Report
      2013 Research-status Report
  • [Presentation] Independence of L-functions and the Nevanlinna characteristic

    • Author(s)
      名越弘文
    • Organizer
      日本数学会2013年度秋季総合分科会
    • Place of Presentation
      愛媛大学
    • Related Report
      2013 Research-status Report
  • [Presentation] Combining three theorems on the joint universality of L-functions

    • Author(s)
      名越弘文
    • Organizer
      日本数学会2014年度年会
    • Place of Presentation
      学習院大学
    • Related Report
      2013 Research-status Report

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

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