2015 Fiscal Year Final Research Report
Study on arithmetic theory of automorphic forms of several variables
| Project/Area Number |
25400031
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Kinki University |
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Principal Investigator |
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Keywords | 保型形式 |
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| Outline of Final Research Achievements |
The aim of this study is to extend Serre’s theory of mod p or p-adic modular forms to the case of modular forms of several variables. In the previous study we determined the structure of the algebra of mod p modular forms in the case of Siegel modular forms which is a typical example of such modular forms. Moreover we determined the structure of such algebra in the case of Hermitian modular forms whose based field is the Gaussian field. Based on these results, we extended the notion of the theta operator and got some results on mod p kernel of such operator. This is defined as the image of the theta operator is congruent zero modulo some prime p. We could get a lot of such examples, for example, Igusa’s weight 35 cusp form and theta series for the Leech lattice are mod 23 kernel of the theta operator. We also clarified the relation between the weight and the congruence prime.
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| Free Research Field |
代数学
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