1999 Fiscal Year Final Research Report Summary
Studies on unified theory of zeta functions
| Project/Area Number |
10640009
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
KUROKAWA Nobushige Graduate School of Science and Engineering, TOKYO INSTITUTE OF TECHNOLOGY, Prof., 大学院・理工学研究科, 教授 (70114866)
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| Co-Investigator(Kenkyū-buntansha) |
MIZUMOTO Graduate School of Science and Engineering, TOKYO INSTITUTE OF TECHNOLOGY, Associate Prof., 大学院・理工学研究科, 助教授 (90166033)
MORITA Takehiko Graduate School of Science and Engineering, TOKYO INSTITUTE OF TECHNOLOGY, Associate Prof., 大学院・理工学研究科, 助教授 (00192782)
SAITO Shuji Graduate School of Science and Engineering, TOKYO INSTITUTE OF TECHNOLOGY, Prof., 大学院・理工学研究科, 教授 (50153804)
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| Project Period (FY) |
1998 – 1999
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| Keywords | zeta function / category / spectrum / unified theory / arithmetical algebraic geometry |
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| Research Abstract |
We studied the unified theory of zeta functions.
Kurokawa studied categorical aspects. Saito studied arithmetical aspects. Morita studied analytical aspects. Mizumoto studied algebraic aspects. We sketch their studies.
Kurokawa published a study on the spectra of Laplace operators of categories containing the semipositivity and the asymptotic spectral distribution. The Laplace operator of a category is a symmetrical matrix consisting of the number of arrows between two objects and its properties are interesting from many view points. Kurokawa studied also Selberg zeta functions, and obtained an explicit formula for the multiplicities of specta. A general theory of zeta functions of algebraic systems. Mizumoto studied orders of zeros of zeta functions at the center of the functional equations, and obtained the unboundedness. Morita made the analytic continuation of the zeta function associated to a two dimensional billiard. Saito studied arithmetical algebraic geometry around algebraic cycles.
These studies present a frame for the unified theory of zeta functions.
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Research Products
(14 results)
