| Project/Area Number |
23340010
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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 九州大学, 数理(科)学研究科(研究院), 教授 (70202017)
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| Co-Investigator(Renkei-kenkyūsha) |
MATSUMOTO Makoto 広島大学, 理学研究科, 教授 (70231602)
MURAKAMI Jun 早稲田大学, 理工学術院, 教授 (90157751)
NAGATOMO Kiyokazu 大阪大学, 情報科学研究科, 准教授 (90172543)
HOSONO Shinobu 東京大学, 数理科学研究科, 准教授 (60212198)
HIKAMI Kazuhiro 九州大学, 数理学研究院, 准教授 (60262151)
TAGUCHI Yuichiro 東京工業大学, 理工学研究科, 教授 (90231399)
TAKATA Toshie 九州大学, 数理学研究院, 准教授 (40253398)
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| Project Period (FY) |
2011-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥13,650,000 (Direct Cost: ¥10,500,000、Indirect Cost: ¥3,150,000)
Fiscal Year 2015: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2014: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2013: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2012: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2011: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
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| Keywords | モジュラー形式 / 準モジュラー形式 / 多重ゼータ値 / 共系場理論 / 位相不変量 / 多重ベルヌーイ数 / 頂点作用素代数 / 有限多重ゼータ値 / 共形場理論 / 2重ゼータ値 / 2重アイゼンシュタイン級数 / 楕円曲線 / 擬テータ関数 |
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| Outline of Final Research Achievements |
For modular forms of one variable, we obtained some congruence results on Fourier coefficients of certain meromorphic modular forms, constructed newforms associated to elliptic curves over the rationals which can be written as eta products via differential equations satisfied by modular forms, and found relations between period polynomials of modular forms and double zeta values of level 2. This last result creates a bridge between modular forms and multiple zeta values. For multiple zeta values proper, we obtained a formula for the height one MZV in terms of MZVs of maximal height, defined and studied a kind of sibling function of the so called Arakawa-Kaneko zeta function, and studied basic properties of finite multiple zeta values. Notably, by introducing symmetric multiple zeta values, we proposed an astonishing main conjecture in the theory of finite multiple zeta values.
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