Studies on the hypergeometric diffeential equations considering the application for the coding theory
| Project/Area Number |
14540153
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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 |
Basic analysis
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| Research Institution | Chiba University |
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Principal Investigator |
SHIGA Hironori Chiba University, Graduate School of Science and Technology, Professor, 大学院・自然科学研究科, 教授 (90009605)
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| Co-Investigator(Kenkyū-buntansha) |
MATSUDA Shigeki Chiba University, Faculty of Science, Associate professor, 理学部, 助教授 (90272301)
TSUTSUI Toru Chiba University, Faculty of Science, Lecturer, 理学部, 講師 (00197732)
SUGIYAMA Ken-ichi Chiba University, Faculty of Science, Associate professor, 理学部, 助教授 (90206441)
KITAZUME Masaaki Chiba University, Faculty of Science, Professor, 理学部, 教授 (60204898)
ISHIMURA Ryuichi Chiba University, Faculty of Science, Professor, 理学部, 教授 (10127970)
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| Project Period (FY) |
2002 – 2004
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| Project Status |
Completed (Fiscal Year 2004)
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| Budget Amount *help |
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2004: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2003: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2002: ¥1,500,000 (Direct Cost: ¥1,500,000)
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| Keywords | Schwarz function / Automorphic form / complex multiplication / Hypergeometric Differential Equation / Mirror Symmetry / K3 surface / monodromy / triangle group / フックス型微分方程式 / モノドロミー群 / アンドレ、オールト予想 / ピカール曲線 / 数論的不連続群 / 符号理論 / 暗号システム / 保型形式 / 格子 / 符号 / テータ関数 |
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| Research Abstract |
We obtained the following results in our project.
In general we don't have algebraic values for the Schwarz map of Gauss hypergeometric differential equations foir tan algebraic argument. So we are asked to ansew the question, when we have its algebraic value? It is a difficult problem, and has been studied for many years by many mathematicians. By the study together with professor J.Wolfart in Frankfurt we discovered the problem is closely connected with the action of the CM field on the space of differentials. The results are pubished in (1)and (2).
In 2001 we made a study about the family with 6 parameters of K3 surfaces characterized by the structure of the Picard lattice. We make a research program to obtain some arithmetic application based on the these previous results.
We made a plan of the future research of modular functions induced from the family of K3 surfaces related to reflexive polytopes.
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Report
(4 results)
Research Products
(11 results)
