| Project/Area Number |
06640084
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | HOSEI University |
|---|
Principal Investigator |
HIRAMATSU Toyokazu Engineering, Professor, 工学部, 教授 (40029674)
|
|---|
| 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)
|
|---|
| Project Period (FY) |
1994 – 1996
|
| Project Status |
Completed (Fiscal Year 1996)
|
| Budget Amount *help |
¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 1996: ¥400,000 (Direct Cost: ¥400,000)
Fiscal Year 1995: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1994: ¥1,000,000 (Direct Cost: ¥1,000,000)
|
|---|
| Keywords | Automorphic forms / Algebraic geometric code / rational point / Kloosterman sum / uniform distribution / Sato-Tate conjecture / Fractal dimension / computational complexity / 有限体 / kloasterman和 / Sato-Tate予想 / 多変数保型形式 / ヘッケ作用素 / セルバーグ型等 / 線形符号 / ヒルベルト型保型形式 / セルバーグ型ゼータ関数 / フラクタル |
|---|
| 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.
|
