2014 Fiscal Year Final Research Report
A study on correspondences of automorphic forms by using comparison of explicit dimension formulas
| Project/Area Number |
24740014
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Wakayama University |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Keywords | 保型形式 / 次元公式 |
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| Outline of Final Research Achievements |
In this study, we obtained an explicit dimension formula for spaces of Siegel cusp forms of degree two with respect to paramodular groups of squarefree level, and also a relation between dimensions of spaces of different automorphic forms. As an applications, we proposed two conjectures. First, we proposed a conjecture on a correspondence which preserves L-functions. It is a generalization of a known conjecture for the cases of prime level. Second, we proposed a lifting conjecture for Siegel modular forms with respect to non-split symplectic groups from elliptic cusp forms. In addition, we carried out explicit calculations of L-functions in the case of discriminant 6 and gave numerical evidence of the above conjectures.
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| Free Research Field |
整数論
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