Study on K3 modular forms derived from hypergeometric systems
Project/Area Number |
15K04807
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Algebra
|
Research Institution | Chiba University |
Principal Investigator |
Shiga Hironori 千葉大学, 大学院理学研究院, 名誉教授 (90009605)
|
Project Period (FY) |
2015-04-01 – 2018-03-31
|
Project Status |
Completed (Fiscal Year 2017)
|
Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
|
Keywords | K3 曲面 / 保型関数 / 超幾何微分方程式 / 虚数乗法論 / テータ関数 / 超幾何函数 / テータ函数 / 保型形式 |
Outline of Final Research Achievements |
In the 19th century, Gauss, Abel and Jacobi constructed the theory of elliptic curves and their moduli. It had a big influence in mathematics of 20th century. At present, it is developed to the higher dimensional analogues. The K3 surface is the 2-dimensional analogue of the elliptic curve. On the other hand, Hilbert proposed his 12th problem in 1901, it was an important proposal in number theory. In 1960's, Shimura gave a big contribution for this problem. But the Hilbert 12th problem iself is still open. In our research project, we could give a visualization of Shimura's theory and constructed a series of explicit examples.
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Report
(4 results)
Research Products
(16 results)
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[Book] 保型関数2017
Author(s)
志賀弘典
Total Pages
273
Publisher
共立出版
ISBN
9784320112049
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