Research on limit theorems for random sequences arising from number theory

• Project/Area Number: 22540128
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Osaka University
• Principal Investigator: SUGITA Hiroshi 大阪大学, 理学(系)研究科(研究院), 教授 (50192125)
• Co-Investigator(Renkei-kenkyūsha): MORITA Takehiko 大阪大学, 大学院理学研究科, 教授 (00192782) ; TAKANOBU Satoshi 金沢大学, 大学院自然科学研究科, 教授 (40197124) ; SHIRA Tomoyuki 九州大学, マス・フォア・インダストリ研究所, 教授 (70302932) ; FUKUYAMA Katusi 神戸大学, 大学院理学研究科, 教授 (60218956)
• Research Collaborator: TRINH Khanh Duy 九州大学, マス・フォア・インダストリ研究所, 助教 (00726127)
• Project Period (FY): 2010-04-01 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000); Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2010: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
• Keywords: 極限定理 / 密度定理 / 数論 / ランダム行列 / 概周期関数 / 一般ディリクレ級数 / スペクトル測度 / 確率論 / 極限周期的算術関数 / 有限整アデール環 / ランダム・ワイル・サンプリング

Outline of Final Research Achievements

Probability theory has dealt with problems arising from random phenomena in nature and society, but this research seeks origins of probability in objects of number theory, such as density theorems and almost periodic functions. As a result, we could establish the framework to deal with density theorems and almost periodic functions and discover some new probabilistic limit theorems about them.

Research Products

• [Journal Article] On convergence of Fourier series of Besicovitch almost periodic functions (2013)
  • Author(s): Trinh Khanh Duy
  • Journal Title: Lith. Math. J. Volume: 53-3
  • Peer Reviewed
• [Journal Article] On the distribution of k-th power free integers (2013)
  • Author(s): Trinh Khanh Duy
  • Journal Title: Osaka J. Math. Volume: 50-3
  • Peer Reviewed
• [Journal Article] On the distribution of k-th power free integers, II (2012)
  • Author(s): Trinh Khanh Duy, Satoshi Takanobu
  • Journal Title: Osaka Journal of Mathematics Volume: (掲載決定)(未定)
  • NAID: 120005327216
  • Peer Reviewed
• [Journal Article] On the distribution of k-th power free integers (2011)
  • Author(s): Trinh Khanh Duy
  • Journal Title: Osaka Journal of Mathematics Volume: 48-4 Pages: 1027-1045
  • Peer Reviewed
• [Journal Article] Limit-periodic arithmetical functions and the ring of finite integral adeles (2011)
  • Author(s): Trinh Khanh Duy
  • Journal Title: Lithuanian Mathematical Journal Volume: 51-4 Issue: 4 Pages: 486-506
  • DOI: 10.1007/s10986-011-9143-3
  • Peer Reviewed
• [Presentation] On random Jacobi matrices related to Gaussian beta ensembles (2014)
  • Author(s): Trinh Khanh Duy
  • Organizer: 確率論シンポジウム
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2014-12-19
• [Presentation] Central limit theorem for moments of spectral measures of Gaussian Wigner matrices (2013)
  • Author(s): Trinh Khanh Duy
  • Organizer: 大阪大学確率論セミナー
  • Place of Presentation: 大阪大学理学部
  • Year and Date: 2013-07-16
• [Presentation] 確率と乱数 (2013)
  • Author(s): 杉田洋
  • Organizer: 日本数学会年会
  • Place of Presentation: 京都大学
  • Year and Date: 2013-03-24
  • Invited
• [Presentation] モンテカルロ法、乱数、および疑似乱数 (2012)
  • Author(s): 杉田洋
  • Organizer: 慶應義塾大学自然科学研究教育センター講演会（第16回）
  • Place of Presentation: 慶應義塾大学日吉キャンパス
  • Year and Date: 2012-05-10
  • Invited
• [Presentation] Carleson's Theorem for General Dirichlet Series (2011)
  • Author(s): Trinh Khanh Duy
  • Organizer: The 5^<th> International Conference in Honour of J.Kubilius
  • Place of Presentation: Palanga(リトアニア共和国)
  • Year and Date: 2011-09-05
• [Presentation] モンテカルロ法,乱数,および疑似乱数 (2011)
  • Author(s): 杉田洋
  • Organizer: 東北大学大学院理学研究科数学教室談話会
  • Place of Presentation: 東北大学,仙台,宮城県(招待講演)
  • Year and Date: 2011-07-11
• [Presentation] On Value Distributions of General Dirichlet Series (2011)
  • Author(s): Trinh Khanh Duy, Hiroshi Sugita
  • Organizer: 解析数論セミナー
  • Place of Presentation: 名古屋大学大学院多元数理科学研究科
  • Year and Date: 2011-03-03
• [Presentation] Besicovitch's limit periodic functions and L^q-spaces over the ring of finite integral adeles (2010)
  • Author(s): Trinh Khanh Duy
  • Organizer: Number Theory and Probability
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2010-09-15
• [Book] Monte Carlo method, Random number, and Pseudorandom generator (2011)
  • Author(s): Hiroshi Sugita
  • Total Pages: 133
  • Publisher: Mathematical Society of Japan
• [Remarks] Hiroshi SUGITA Work in Mathematics
  • URL: http://www.math.sci.osaka-u.ac.jp/~sugita/mathematics.html
• [Remarks] Hiroshi SUGITA Work in Mathematics
  • URL: http://www.math.sci.osaka-u.ac.jp/~sugita/mathematics.html
• [Remarks]
  • URL: http://homepage.mac.com/hiroshi_sugita/mathematics.html
• [Remarks]
  • URL: http://homepage.mac.com/hiroshi_sugita/mathematics.html