| Project/Area Number |
15K17515
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Kyushu University |
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Principal Investigator |
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 楕円曲線 / モジュラー形式 / 高速計算 / 計算代数 / 計算機数論 / 保型性 |
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| Outline of Final Research Achievements |
According to this research project, we provided some fast implementation to compute several family of elliptic curves over algebraic number field, and elliptic modular forms with associated Hecke algebra. More precisely, we achieved to get two efficient algorithm: (i) Searching all elliptic curves having everywhere good reduction with given conductor, and (ii) Calculating maximal orders of Hecke algebra with prescribed ramification of primes over the rational field. In addition, using several refinements by this project, we get an implementation of pairings (from elliptic curves) at the high security bit levels.
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