Research on the theory of modular forms and modular functions using Mathematica
Project/Area Number |
19540040
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Single-year Grants |
Section | 一般 |
Research Field |
Algebra
|
Research Institution | Kyushu University |
Principal Investigator |
KOIKE Masao Kyushu University, 大学院・数理学研究院, 教授 (20022733)
|
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)
|
Project Period (FY) |
2007 – 2010
|
Project Status |
Completed (Fiscal Year 2010)
|
Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2008: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2007: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
|
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 / 2進的保型形式 / アトキンの方法 / 3進的保型形式 / トンプソン級数 / フリッケ群 / 超特異多項式 / 2進的な保型形式 / 級数展開 / フーリエ係数 / テータ級数 / 合同式 |
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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Report
(6 results)
Research Products
(17 results)