Various modular forms and these applications for Number Theory
Project/Area Number |
23740011
|
Research Category |
Grant-in-Aid for Young Scientists (B)
|
Allocation Type | Multi-year Fund |
Research Field |
Algebra
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Research Institution | Keio University (2013) The University of Tokyo (2011-2012) |
Principal Investigator |
TAKAI Yuuki 慶應義塾大学, 理工学部, 特任助教 (90599698)
|
Project Period (FY) |
2011 – 2013
|
Project Status |
Completed (Fiscal Year 2013)
|
Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
|
Keywords | 保型形式 / Galois 群 / Hilbert 保型形式 / 相対類数 / 保型 L-関数 / Sturm の定理 / L-関数の特殊値 / Abel 多様体 / 類数問題 / 保型L-関数 / Hilbert モジュラー形式 / 半整数ウエイト保型形式 / アーベル多様体 / 相対類数の非可除性 / 相対岩澤不変量の消滅 / 半整数ウエイト Hilbert 保型形式 / L-関数の特殊値 / 重さ半整数の保型形式 / Galois 表現 |
Research Abstract |
Combining properties of modular forms and Galois groups, I studied some applications for number theory. In particular, the main purpose is to extend some arithmetic results on the rational field to them on more general fields. To do this, I studied property of Hilbert modular forms as a tool and applied to the class number problem for CM quadratic extension.
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Report
(4 results)
Research Products
(35 results)