| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Outline of Final Research Achievements |
We studied in details the second main terms in counting discriminants of certain families of number fields. The results include: On the counting function for non-commutative sextic Galois fields, we get an evidence that there might exist the tertiary main term. On the counting function for relative cubic extensions, when the base field is a quadratic field, we determined the second main term; over a general number field, we determined the second main term for a smoothed counting function. We have several more results. As a related problem, we discover a simple method to evaluate certain exponential sums associated with prehomogeneous vector spaces.
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