Analytic properties of arithmetic zeta functions and geometric symmetry
| Project/Area Number |
21740004
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Tokyo Institute of Technology (2012)
The University of Tokyo (2009-2011) |
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Principal Investigator |
SUZUKI Masatoshi 東京工業大学, 大学院・理工学研究科, 准教授 (30534052)
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| Project Period (FY) |
2009 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 数論 / ゼータ関数 / 解析接続 / 関数等式 / 零点分布 / 代数学 / 自己相反多項式 / 再生核ヒルベルト空間 / ハミルトニアン / リーマン予想 / 楕円曲線 / 零点 |
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| Research Abstract |
Zeta functions are a group of certain special functions having its origin in the Riemann zeta function. They play important roles in various fields of mathematics. In this research project, we studied about important analytic properties of arithmetic zeta functions like analytic continuations and distributions of thier poles and zeros. As the results, we established a new bridge between analytic properties of zeta functions in number theory and modern harmonic analysis, and obtained new results on the distribution of zeros of so-called high-rank zeta functions which are direct generalizations of the Riemann zeta function.
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Report
(5 results)
Research Products
(50 results)
