| Budget Amount *help |
¥9,360,000 (Direct Cost: ¥7,200,000、Indirect Cost: ¥2,160,000)
Fiscal Year 2016: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2015: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2014: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2013: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
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| Outline of Final Research Achievements |
Focusing mainly on zeta functions of prehomogeneous vector spaces, we investigate what kind of zeta functions may be associated with representations of algebraic groups, and their arithmetic significance when they exist. Our primary achievement is an application of density theorems. For counting functions of discriminants of cubic fields, we obtained a strong quantitative result. We also studied exponential sums appearing in the functional equation of the zeta function. We developed a simple and effective method to compute them, and give a variety of new explicit formulas.
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