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Analytic properties of zeta functions

Research Project

Project/Area Number 24740029
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Algebra
Research InstitutionTokyo University of Science (2012-2013, 2015)
The University of Tokyo (2014)

Principal Investigator

Nakamura Takashi  東京理科大学, 理工学部, 講師 (50532355)

Project Period (FY) 2012-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
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: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
KeywordsMultiple zeta values / Multiple zeta functions / Value distribution / Universality / divisible distributions / Zeta distributions / ゼータ関数 / 実零点 / 関数等式 / 多重ゼータ関数 / 特性関数 / 無限分解可能分布 / 普遍性 / ゼータ分布 / 値分布
Outline of Final Research Achievements

The research I did is divided into 3 parts: (1) Multiple zeta values, Multiple zeta functions and their functional relations, (2) Value distribution, (especially, Universality) of zeta functions and L-functions, (3) Infinitely divisible distributions, Zeta distributions.
These are corresponding to 2010 Mathematics Subject Classification 11M06, 11M26, 11M32, 11M35.

Report

(5 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (22 results)

All 2015 2013 2012 Other

All Journal Article (11 results) (of which Peer Reviewed: 11 results) Presentation (9 results) (of which Int'l Joint Research: 2 results,  Invited: 5 results) Remarks (2 results)

  • [Journal Article] A modified Riemann zeta distribution in the critical strip2015

    • Author(s)
      Takashi Nakamura
    • Journal Title

      Proc. Amer.Math. Soc

      Volume: 143 Issue: 2 Pages: 897-905

    • DOI

      10.1090/s0002-9939-2014-12279-9

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A complete Riemann zeta distribution and the Riemann hypothesis2015

    • Author(s)
      Takashi Nakamura
    • Journal Title

      Bernoulli Journal

      Volume: 21

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Remarks on double zeta values of level 22013

    • Author(s)
      Takashi Nakamura, Koji Tasaka
    • Journal Title

      J. Number Theory

      Volume: 133 Issue: 1 Pages: 4854-4854

    • DOI

      10.1016/j.jnt.2012.07.005

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Self-approximation for the Riemann zeta function2013

    • Author(s)
      Takashi Nakamura, Lukasz Pankowski
    • Journal Title

      Bulletin of the Australian Mathematical Society

      Volume: 87 Issue: 3 Pages: 452461-452461

    • DOI

      10.1017/s0004972712000846

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] A quasi-infinitely divisible characteristic function and its exponentiation2013

    • Author(s)
      Takashi Nakamura
    • Journal Title

      Statistics and Probability Letters

      Volume: 83 Issue: 10 Pages: 22562259-22562259

    • DOI

      10.1016/j.spl.2013.06.015

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Multidimensional Shintani zeta functions and zeta distributions on R^d2013

    • Author(s)
      Takahiro Aoyama, Takashi Nakamura
    • Journal Title

      Tokyo Journal Mathematics

      Volume: 36 Pages: 521538-521538

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Behaviors of multivariable finite Euler products in probabilistic view2013

    • Author(s)
      Takahiro Aoyama, Takashi Nakamura
    • Journal Title

      Mathematische Nachrichten

      Volume: 286 Issue: 17-18 Pages: 16911700-16911700

    • DOI

      10.1002/mana.201200151

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Erratum to: The generalized strong recurrence for non-zero rational parameters2012

    • Author(s)
      T. Nakamura and L. Pankowski
    • Journal Title

      Arch. Math. (Basel)

      Volume: 99 Issue: 6 Pages: 43-47

    • DOI

      10.1007/s00013-010-0205-2

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Zeros of zeta functions and zeta distributions on R^d2012

    • Author(s)
      T. Aoyama and T. Nakamura
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: B34 Pages: 39-48

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] The generalized strong recurrence and the Riemann Hypothesis'2012

    • Author(s)
      T. Nakamura
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: B34 Pages: 265-276

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] A simple proof of the functional relation for the Lerch type Tornheim double zeta function2012

    • Author(s)
      T. Nakamura
    • Journal Title

      Tokyo Journal Mathematics

      Volume: 35 Issue: 2 Pages: 333-337

    • DOI

      10.3836/tjm/1358951322

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] Real zeros of Hurwitz-Lerch zeta and Hurwitz-Lerch type of Euler-Zagier double zeta functions2015

    • Author(s)
      Takashi Nakamura
    • Organizer
      The conference of Zeta Functions of Several Variables and Applications
    • Place of Presentation
      名古屋大学(愛知県)
    • Year and Date
      2015-11-12
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Joint universality for Lerch zeta-functions2015

    • Author(s)
      Takashi Nakamura
    • Organizer
      French-Japanese Workshop on multiple zeta functions and applications
    • Place of Presentation
      Saint-Etienne (France)
    • Year and Date
      2015-09-07
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Real zeros of Hurwitz-Lerch zeta and Hurwitz-Lerch type of Euler-Zagier double zeta functions2015

    • Author(s)
      Takashi Nakamura
    • Organizer
      第8回多重ゼータ研究集会
    • Place of Presentation
      大阪体育大学
    • Year and Date
      2015-02-19
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] A complete Riemann zeta distribution and the Riemann hypothesis2015

    • Author(s)
      Takashi Nakamura
    • Organizer
      第8回ゼータ若手研究集会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2015-02-16
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Multidimensional zeta distributions and infinite divisibility2012

    • Author(s)
      Takashi Nakamura
    • Organizer
      解析的整数論とその周辺
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2012 Research-status Report
  • [Presentation] Zeros of Epstein zeta-functions2012

    • Author(s)
      Takashi Nakamura
    • Organizer
      国際研究集会 ゼータ関数 2012
    • Place of Presentation
      東京工業大学大学大岡山キャンパス
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] A modified Riemann zeta distribution in the critical stri

    • Author(s)
      Takashi Nakamura
    • Organizer
      解析的整数論ー超越関数の数論的性質とその応用
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2013 Research-status Report
  • [Presentation] 完備リーマンゼータ分布とリーマン予想

    • Author(s)
      Takashi Nakamura
    • Organizer
      無限分解可能過程に関連する諸問題
    • Place of Presentation
      統計数理研究所
    • Related Report
      2013 Research-status Report
  • [Presentation] A modified Riemann zeta distribution and the exponential distribution

    • Author(s)
      Takashi Nakamura
    • Organizer
      4th Ritsumeikan-Monash Symposium on Probability and Related Fields
    • Place of Presentation
      立命館大学
    • Related Report
      2013 Research-status Report
    • Invited
  • [Remarks] Takashi Nakamura

    • URL

      https://sites.google.com/site/takashinakamurazeta/

    • Related Report
      2015 Annual Research Report 2014 Research-status Report
  • [Remarks] Takashi Nakamura

    • URL

      https://sites.google.com/site/takashinakamurazeta/

    • Related Report
      2013 Research-status Report

URL: 

Published: 2013-05-31   Modified: 2019-07-29  

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