2013 Fiscal Year Final Research Report
Various modular forms and these applications for Number Theory
| Project/Area Number |
23740011
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Keio University (2013)
The University of Tokyo (2011-2012) |
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Principal Investigator |
TAKAI Yuuki 慶應義塾大学, 理工学部, 特任助教 (90599698)
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| Project Period (FY) |
2011 – 2013
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| 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 |
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| 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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