|Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
|Outline of Final Research Achievements
Class numbers of cyclotomic fields are important object of research in Algebraic Number Theory. As to the computation of them, cyclotomic fields of prime conductors were main target of research. In this project, we enlarged the area of computation to (minus parts of) class numbers of cyclotomic fields of prime power conductors. We focused on the Hypothesis, posed by Prof. H.Ichimura, that the relative minus-part class numbers of the prime power cyclotomic fields are relatively prime to each other for all prime powers.
On our project, we performed an extensive computation of the class numbers for prime-power cyclotomic fields, and verified that the above Hypothesis is (almost) valid in the range of our computation, finding only one exception to the Hypothesis.