Additive decomposition and positivity for zeta functions
| Project/Area Number |
25800007
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | ゼータ関数 / 零点分布 / リーマン予想 / 正準系 / スペクトル逆問題 / 数論 / ハミルトニアン / 零点 |
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| Outline of Final Research Achievements |
A group of special functions called zeta functions is one of the major research areas in number theory. The Riemann zeta function and Dirichlet L functions are typical examples of zeta functions. In this research project, we have studied the distributions of the zeros of the zeta functions, which are important in number theory, with the theory of certain systems of ordinary linear differential equations. As one of the achievements, a new theoretical framework relating number theory with function analysis was obtained. In addition, a new discovery was made about the distribution of the imaginary parts of the zeros of certain special zeta functions.
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Report
(5 results)
Research Products
(23 results)
