Number theory from a viewpoint of computation of modular forms
| Project/Area Number |
26400008
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | University of Toyama |
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Principal Investigator |
Kimura Iwao 富山大学, 大学院理工学研究部(理学), 准教授 (10313587)
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | モジュラー形式 / コンピューター / モジュラ形式の零点 / Fricke群 / Eisenstein級数 / Maass波動形式 / Maass波動カスプ形式 / 偶Artin表現 / 重さ1のモジュラ形式 / 法l Galois表現の計算 |
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| Outline of Final Research Achievements |
The point of this research is to study some problems on number theory which are related to elliptic modular forms via explicit numerical/symbolic computation using computers. On the first year of this three years project, I mainly concerned on the computation of 2 dimensional complex Artin representation of the Galois group of the rationals associated with the Hecke eigen cuspform of weight 1. It is of special interest if those image are non-solvable. If the conductor of this representation are square free, the explicit bound of order of computations. In the second year, I mainly studied a numerical method to compute Maass waveforms. I found a numerical instability of the method I took makes things complicated. In the last year, I considered zeros of modular forms on Fricke groups and obtained some extension of results which are known by prior study.
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Report
(4 results)
Research Products
(13 results)
