| Project/Area Number |
22540033
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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 | Sophia University |
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Principal Investigator |
TSUZUKI Masao 上智大学, 理工学部, 准教授 (80296946)
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| Co-Investigator(Kenkyū-buntansha) |
TSUNOGAI Hiroshi 上智大学, 理工学部, 教授 (20267416)
角皆 宏 上智大学, 理工学部, 教授 (20267412)
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| Co-Investigator(Renkei-kenkyūsha) |
MORIYAMA Tomonori 大阪大学, 大学院理学研究科, 准教授 (80384171)
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| Project Period (FY) |
2010-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | Ｌ関数特殊値 / 保型形式の周期 / 相対跡公式 / 軌道積分の移送 / Ｌ関数 / 保型形式の周期積分 / 中心Ｌ値 / 新谷関数 / グリーン関数 / L関数の特殊値 / IV型領域の保型形式 / 標準L函数の中心値 / マース波動表現 |
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| Outline of Final Research Achievements |
(1)We studied the product of central values of standard L-function and their quadratic twist(or its first derivative) associated with holomorphic Hilbert modular forms over a general totally real number field. We developed an explicit relative trace formula whose spectral side encodes such quantities and obtained several applications, which includ the equidistribution of Satake parameters of automorphic represnetations and explicit subconvex exponent of certain central L-values in the weight aspect.
(2) We studied the holomorphic scalar valued cusp forms on type IV bounded symmetric domain from the aspect of their Fourier coefficients. We proposed a good normalization of certain weighted average of Fourier coefficients, which is compatible to known normalizations of classical modular forms. We developed a certain summation formula whose spectral side encodes the square of the normalized Fourier coefficients and the central values of the standard L-functions.
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