| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2016: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
|
|---|
| Outline of Final Research Achievements |
For given sequence of real numbers, multiplying a real number and investigate the distribution of fractional part. This is the thema of uniform distribution theory.
For various sequences, the limit distribution is the uniform distribution for almost every multiplied real number, and we analyse the speed of convergence toward the uniform distribution by using the notion of discrepancies. We have already prove the law of the iterated logarithm for discrepancies for geometric progressions, and proved the formula which give the limsup constant when the ratio is large. In this project, we found several ratios for which the limsup constant is different from the value given by the formula. We also proved the existence of the sequence which realize the given speed of convergence of discrepancies.
|
