Randomness in number theory

2015 Fiscal Year Final Research Report

• Project/Area Number: 24340017
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Partial Multi-year Fund
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Kobe University
• Principal Investigator: Fukuyama Katusi 神戸大学, 理学(系)研究科(研究院), 教授 (60218956)
• Co-Investigator(Kenkyū-buntansha): NAKADA HITOSHI 慶應義塾大学, 理工学部, 教授 (40118980) ; SUGITA HIROSHI 大阪大学, 大学院理学研究科, 教授 (50192125) ; KAJINO NAOTAKA 神戸大学, 大学院理学研究科, 准教授 (90700352)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 確率論 / 一様分布 / 差異量

Outline of Final Research Achievements

We investigated the uniform distributedness of geometric progression and made research on the law of the iterated logarithm which discribes the deviation from the uniform distribution. We tried to determine the constant and suceeded in having the general formula of the constant in the case the absolute value of the ratio is large.
It solves the problem on the speed of convergence to the uniform distribution when the ratio is large.

Free Research Field

確率論