Analytic properties for several types of zeta-functions

• Project/Area Number: 21740024
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: Tokyo University of Science
• Principal Investigator: NAKAMURA Takashi 東京理科大学, 理工学部, 助教 (50532355)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2011: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000); Fiscal Year 2010: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: ゼータ関数 / 値分布 / 多重ゼータ関数 / 強再帰性 / 普遍性 / 無限分解可能性 / 無限分解

Research Abstract

I obtained some results of universality, hybrid universality and self-approximation for several types of zeta-functions.

Research Products

• [Journal Article] On universality of linear combinations of L-functions (2012)
  • Author(s): 中村隆, Lukasz Pankowski
  • Journal Title: Monatshefte fuer Mathematik Volume: no.3 Pages: 433-446
• [Journal Article] Applications of hybrid universality to multivariable zeta-functions (2012)
  • Author(s): 中村隆, Lukasz Pankowski
  • Journal Title: J. Number Theory Volume: no.11 Pages: 2151-2161
• [Journal Article] On universality of linear combinations of $L$-functions (2012)
  • Author(s): 中村隆, Lukasz Pankowski
  • Journal Title: Monatshefte fuer Mathematik Volume: 165 Pages: 433-446
  • Peer Reviewed
• [Journal Article] The universality for linear combinations of Lerch zeta functions and the Tornheim-Hurwitz type of double zeta functions (2011)
  • Author(s): 中村隆
  • Journal Title: Monatshefte fuer Mathematik Volume: no.2 Pages: 167-178
• [Journal Article] Some topics related to universality of L-functions with an Euler product (2011)
  • Author(s): 中村隆
  • Journal Title: Analysis Volume: no.1 Pages: 31-41
• [Journal Article] Applications of hybrid universality to multivariable zeta-functions (2011)
  • Author(s): 中村隆, Lukasz Pankowski
  • Journal Title: Journal of Number Theory Volume: 131 Pages: 2151-2161
  • Peer Reviewed
• [Journal Article] The generalized strong recurrence for non-zero rational parameters (2010)
  • Author(s): 中村隆
  • Journal Title: Arch. Math.(Basel) Volume: no.6 Pages: 549-555
• [Journal Article] Some formulas related to Hurwitz-Lerch zeta functions (2010)
  • Author(s): 中村隆
  • Journal Title: The Ramanujan Journal Volume: no.3 Pages: 285-302
• [Journal Article] The generalized strong recurrence for non-zero rational parameters (2010)
  • Author(s): 中村隆
  • Journal Title: Archiv der Mathematik Volume: 95 Pages: 549-555
  • Peer Reviewed
• [Journal Article] Some topics related to universality for L-functions with Euler product (2010)
  • Author(s): 中村隆
  • Journal Title: Analysis International mathematical journal of analysis and its applications Volume: 31 Pages: 31-41
  • Peer Reviewed
• [Journal Article] Some formulas related to Hurwitz-Lerch zeta functions (2010)
  • Author(s): 中村隆
  • Journal Title: The Ramanujan Journal 21-3 Pages: 285-302
  • Peer Reviewed
• [Presentation] 多重ゼータ関数と多次元ゼータ分布 (2011)
  • Author(s): 中村隆
  • 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
  • Year and Date: 2011-11-11
• [Presentation] Zeros of multiple zeta functions (2011)
  • Author(s): 中村隆
  • Organizer: 解析的整数論-数論的関数の多重性に関連して
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2011-11-01
• [Presentation] Zeros of multiple zeta functions (2011)
  • Author(s): 中村隆, Lukasz Pankowski
  • Organizer: The Fifth International Conference in Honor of J. Kubilius
  • Place of Presentation: Conference Center of Vilnius University, Lithuania
  • Year and Date: 2011-09-09
• [Presentation] Multidimensional zeta distributions and infinite divisibility (2011)
  • Author(s): 中村隆, Takahiro Aoyama
  • Organizer: The Fifth International Conference in Honor of J. Kubilius
  • Place of Presentation: Conference Center of Vilnius University, Lithuania
  • Year and Date: 2011-09-08
• [Presentation] The generalized strong recurrence and the Riemann hypothesis (2010)
  • Author(s): 中村隆
  • Organizer: Functions in Number Theory and Their Probabilistic Aspects
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2010-12-17
• [Presentation] The generalized strong recurrence for the Riemann zeta function (2010)
  • Author(s): 中村隆
  • Organizer: Number Theory and Probability
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2010-09-13
• [Presentation] Zeros and universality for the Euler-Zagier-Hurwitz type of multiple zeta functions (2009)
  • Author(s): 中村隆
  • Organizer: Zeta Function Days in Seoul
  • Place of Presentation: Yonsei University, Korea
  • Year and Date: 2009-09-02
• [Presentation] The joint universality and the generalized self-similarity for L-functions (2009)
  • Author(s): 中村隆
  • Organizer: 2009 Graduate Workshop on Zeta Functions, L-Functions and their Applications
  • Place of Presentation: Utah Valley University, USA
  • Year and Date: 2009-06-04
• [Remarks]
  • URL: http://www.ma.noda.tus.ac.jp/u/tn/
• [Remarks]
  • URL: http://www.ma.noda.tus.ac.jp/u/tn/
• [Remarks]
  • URL: http://www.ma.noda.tus.ac.jp/u/tn/