2009 Fiscal Year Final Research Report
Green functions and relative trace formulas
| Project/Area Number |
18540049
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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 Sophia University, 理工学部, 准教授 (80296946)
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| Co-Investigator(Kenkyū-buntansha) |
GOMI Yasushi 上智大学, 理工学部, 講師 (50276515)
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| Co-Investigator(Renkei-kenkyūsha) |
MORIYAMA Tomonori 大阪大学, 理学研究科, 准教授 (80384171)
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| Project Period (FY) |
2006 – 2009
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| Keywords | グリーン函数 / 相対跡公式 / 一般超幾何級数 / エル関数 |
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| Research Abstract |
We develop a version of relative trace formula for symmetric spaces associated with indefinite unitary groups of arbitrary real rank and for orthogonal groups of real rank one. As an application, we prove two kinds of asymptotic formulas ; (1) It is proved that the Plancherel formula of the symmetric space for unitary group is approximated by certain sequence of discrete measures arising from the average of square norm of period integrals of automorphic forms on an arithmetic quotient of the unitary group. (2) We showed an asymptotic formula for certain average of period integrals of L2-normalized Laplace eigenfunctions on an arithmetic quotient of rank one orthogonal group ; the formula should be regarded as an analogue of Weyl's law for spectral counting function for multiplicity of Laplace eigenvalues.
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