2011 Fiscal Year Final Research Report
Explicit trace formulas for Hecke operators on spaces of modular forms of several variables
| Project/Area Number |
20740007
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Kanazawa University |
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Principal Investigator |
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| Project Period (FY) |
2008 – 2011
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| Keywords | 代数学 / 整数論 / 保型形式 / 跡公式 |
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| Research Abstract |
In this study, we have explicitly calculated geometric sides of trace formulas, in order to derive concrete numerical values of traces of Hecke operators on spaces of Siegel cusp forms of degree two. Therefore, we have obtained arithmetic formulas for contributions of each conjugacy classes in the geometric side. Applying the formulas, we got some results on explicit formulas for dimension of spaces(traces of trivial actions) and we partly solved computations for traces of involutions as certain Hecke operators.
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