2010 Fiscal Year Final Research Report
Research on the theory of modular forms and modular functions using Mathematica
| Project/Area Number |
19540040
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 |
KOIKE Masao Kyushu University, 大学院・数理学研究院, 教授 (20022733)
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| Co-Investigator(Kenkyū-buntansha) |
BANNAI Eiichi 九州大学, 大学院・数理学研究院, 学術研究者 (10011652)
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| Project Period (FY) |
2007 – 2010
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| Keywords | 保型形式 / 保型関数 / p進整数 / p進的保型形式 / マッカイ・トンプソン級数 / extremalな保型形式 |
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| Research Abstract |
We find the congruences between extremal modular forms and theta series of special types modulo powers of 2 and 3.This assertion enables us to prove that 2n-th root of the extremal modular forms of weight n/2 have at least one non integer coefficient.
Let f(z) be a Hauptmodul for level 2 congruence subgroup that has zero at the cusp infinity. We construct the 2-adic modular form F from f(z) by using Atkin's method. We expand F as a formal power series in f(z). We can compute explicitly the 2-adic ordinal of these coefficients of the f-expansion of F.
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