Number theory for representations of algebraic groups and associated zeta functions
| Project/Area Number |
25707002
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (A)
|
| Allocation Type | Partial Multi-year Fund |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Kobe University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2013-04-01 – 2018-03-31
|
| Project Status |
Completed (Fiscal Year 2017)
|
| 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)
|
|---|
| Keywords | ゼータ関数 / 代数群 / 概均質ベクトル空間 / 密度定理 / 指数和 / 代数群の表現 / 数の幾何 / 代数学 / 整数論 / 余正則空間 / 概素数 / 篩 / 代数群の整数論 / 国際情報交換，米国 / 多重ディリクレ級数 |
|---|
| 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.
|
Report
(6 results)
Research Products
(31 results)
