Research on limit theorems for random sequences arising from number theory

2014 Fiscal Year Final Research Report

• 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
• 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

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.

Free Research Field

確率論