1996 Fiscal Year Final Research Report Summary
Hilbert type automorphic forms and its application
| Project/Area Number |
06640084
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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 | HOSEI University |
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Principal Investigator |
HIRAMATSU Toyokazu Engineering, Professor, 工学部, 教授 (40029674)
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| Co-Investigator(Kenkyū-buntansha) |
FUSE Mitsuo Engineering, Lecturer, 工学部, 講師 (00120832)
TANAKA Hisao Engineering, Professor, 工学部, 教授 (70061025)
ANDO Shiro Engineering, Professor, 工学部, 教授 (60061016)
NAGASAKA Kenji Engineering, Professor, 工学部, 教授 (40000187)
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| Project Period (FY) |
1994 – 1996
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| Keywords | Automorphic forms / Algebraic geometric code / rational point / Kloosterman sum / uniform distribution / Sato-Tate conjecture / Fractal dimension / computational complexity |
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| Research Abstract |
Let C be the basic Kloosterman code over any finite field. We proved that the weights of the code C are uniformly distributed with respect to Sato-Tate measure. Further more, by generalizing this result we gave a new code C_n, to be called the hyperkloosterman code (C=C_2), and deduced a uniform distribution theorem for the weights of the codewords of C_n.
In 1981, D.Goppa found a surprising link between coding theory and algebraic geometry. Namely he used rational points on algebraic curves to construct code over a finite field. We gave a short survey of the work done on algebraic geometric codes, automorphic forms and number theory during the last 15 years.
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