| Project/Area Number |
18540055
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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 | Rikkyo University |
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Principal Investigator |
AOKI Noboru Rikkyo University, 理学部, 教授 (30183130)
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| Co-Investigator(Kenkyū-buntansha) |
FUJII Akio 立教大学, 理学部, 教授 (50097226)
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| Project Period (FY) |
2006 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥3,310,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥510,000)
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: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2006: ¥1,100,000 (Direct Cost: ¥1,100,000)
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| Keywords | 数論 / アーベル多様体 / ガウス和 / フェルマー曲面 / 代数的サイクル / Hecke L関数 / Riemann予想 / Davenpot和 / ゼータ関数 / フェルマー曲線 / ヤコビ和 / p進ガンマ関数 / Farey数列 / ディオファンタス方程式 / ファレイ数列 / L関数 / 楕円曲線 / 虚数乗法論 / モーデル・ヴェイユ群 / リーマンゼータ関数 / リーマン予想 |
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| Research Abstract |
We studied some arithmetic problems on abelian varieties defined over number fields. As a result, we obtained a refinement of Silverberg's estimates on the structure of the group of rational points of finite order on abelian varieties with complex multiplication. We also studied the conditions for the congruent zeta function of the Jacobian varieties of Fermat curves over finite fields to be expressed by pure Gauss sums, and succeeded in determining explicit forms of the zeta functions under certain conditions. Further, we studied the distribution of the argument of the Riemann zeta function on the critical line, and obtained some new estimating formula.
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