2011 Fiscal Year Final Research Report
Explicit construction of automorphic forms and its application to number theory and geometry
| Project/Area Number |
21740025
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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 | Kumamoto University |
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Principal Investigator |
NARITA Hiroaki 熊本大学, 大学院・自然科学研究科, 准教授 (70433315)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 整数論 / 保型形式 / テータリフト / ジャッケ・ラングランズ・清水対応 / 双曲多様体 / 対称錐体 / 実数値保型関数 |
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| Research Abstract |
As the main progress of the study on the number theory, I have succeeded in providing examples of the Jacquet-Langlands-Shimizu correspondence for automorphic forms on the symplectic group of degree two and its inner forms by some theta lifting construction of the automorphic forms, which is a joint work with Takeo Okazaki. As for the geometric application, I have given a general construction of real-valued automorphic functions on symmetric cones, which contain real hyperbolic spaces of general dimension. The former achievement can be regarded as very few examples of the guiding principle of the theory of automorphic forms, called "Langlands principle of functoriality". For the latter we have in mind a geometric application such as the embedding of an arithmetic quotient of a hyperbolic space into a real affine space and its generalization to symmetric cone.
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