2010 Fiscal Year Final Research Report
Arithmetic study of modular forms belonging to the Maass space
| Project/Area Number |
21840036
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | The University of Tokushima |
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Principal Investigator |
YOSHINORI Mizuno The University of Tokushima, 大学院・ソシオテクノサイエンス研究部, 准教授 (30546388)
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| Project Period (FY) |
2009 – 2010
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| Keywords | アイゼンシュタイン級数 / ケッヒャー・マース級数 / カトック・サルナック対応 / フーリエ係数 / 類数 / マース空間 / モジュラー形式 |
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| Research Abstract |
We determined a proportional constant which appeares in three dimensional analogue of the Katok-Sarnak type formula.
We studied p-adic Hermitian-Eisenstein series of low weight by using Hecke's convergent factor.
We expressed average values of Eisenstein series over CM points on n-dimensional hyperbolic space in terms of a Dirichlet series whose coefficients are the number of the solutions of quadratic congruences.
We gave a good definition of Koecher-Maass series for indefinite Fourier coefficients of real analytic Siegel-Eisenstein series of degree 2 and weight 2. We then proved a meromorphic continuation and a functional equation of the Koecher-Maass series.
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