| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Outline of Final Research Achievements |
We studied exponential sums associated with prehomogeneous vector spaces. We obtained explicit formulas for several prehomogeneous vector spaces.
We also studied applications to number theory. By developing sieve methods, we obtained two major results: (1) We showed there exist "many" quartic fields whose discriminants have at most eight prime factors. (2) We improved the error term estimate in the counting function for cubic fields. We largely improved the uniform estimate with respect to the splitting conditions of the cubic fields.
We further developed a method for evaluating exponential sums, and obtained a further improvement to sieve methods in question.
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