Study of automorphic forms and zeta functions by using generalized or refined resolvent type trace formulas
| Project/Area Number |
23540020
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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 | Kyushu University |
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Principal Investigator |
GON Yasuro 九州大学, 数理(科)学研究科(研究院), 准教授 (30302508)
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| Co-Investigator(Renkei-kenkyūsha) |
TSUZUKI Masao 上智大学, 理工学部, 准教授 (80296946)
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| Project Period (FY) |
2011 – 2013
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
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| Keywords | 数論 / 保型形式 / ヒルベルトモジュラー曲面 / セルバーグ型ゼータ関数 / スペクトルゼータ関数 / 正規化行列式 / セルバーグ型ディリクレ級数 / セルバーグ跡公式 / ヒルベルトモジュラー群 / ルエル型ゼータ関数 / 素測地線定理 / ワイルの法則 |
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| Research Abstract |
We investigated a generalization or refinement of resolvent type trace formulas, which is useful for studying automororphic forms and zeta functions. Based on our results, we proved analytic properties of zeta functions of Ruelle and Selberg type in one or two variables for Hilbert modular surfaces. Besides, we also proved a prime geodesic type theorem and a regularized determinant formula for restricted Laplacians on Hilbert-Maass forms.
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Report
(4 results)
Research Products
(18 results)
