2010 Fiscal Year Final Research Report
Studies on modular and quasimodular forms arising in various contexts in mathematics and physics
| Project/Area Number |
19340009
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Kyushu University |
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Principal Investigator |
KANEKO Masanobu Kyushu University, 大学院・数理学研究院, 教授 (70202017)
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| Co-Investigator(Renkei-kenkyūsha) |
KOIKE Masao 九州大学, 大学院・数理学研究院, 教授 (20022733)
TAGUCHI Yuichiro 九州大学, 大学院・数理学研究院, 准教授 (90231399)
SAITO Masahiko 神戸大学, 理学部, 教授 (80183044)
TAKATA Toshie 九州大学, 大学院・数理学研究院, 准教授 (40253398)
HOSONO Shinobu 東京大学, 大学院・数理科学研究科, 准教授 (60212198)
HIKAMI Kazuhiro 鳴門教育大学, 准教授 (60262151)
ZAGIER Don ドイツ・マックスプランク研究所, 教授
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| Project Period (FY) |
2007 – 2010
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| Keywords | モジュラー形式 / 準モジュラー形式 / 楕円モジュラー関数 |
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| Research Abstract |
We mainly studied the elliptic modular function, modular forms, and quasimodular forms. In particular, we found a very interesting phenomena concerning the behavior of the j-function at real quadratic numbers. Related topics such as Markoff irrationalities and the caliber of real quadratic fields were studied. Other topics we studied include 2-adic modular forms, quadratic version of Serre's modularity conjecture, monodromies of Painleve equations, mirror symmetries of Calabi-Yau varieties, and free energy of lens spaces, which are related to automorphic forms.
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