2010 Fiscal Year Final Research Report
On automorphic forms on algebraic groups: Arithmetic invariants and automorphic L-functions
| Project/Area Number |
20540031
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Kyoto Sangyo University |
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Principal Investigator |
MURASE Atsushi Kyoto Sangyo University, 理学部, 教授 (40157772)
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| Co-Investigator(Renkei-kenkyūsha) |
NARITA Hiroaki 熊本大学, 自然科学研究科, 准教授 (70433315)
SUGANO Takashi 金沢大学, 理工研究域数物科学系, 教授 (30183841)
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| Research Collaborator |
BERNHARD Heim German University of Technology (Oman), 准教授
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| Project Period (FY) |
2008 – 2010
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| Keywords | 代数群 / 保型形式 / フーリエ展開 / 保型L関数 / 対称性 / ボーチャーズ積 |
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| Research Abstract |
Several invariants are attached to automorphic forms on algebraic groups. These invariants and relationships between them are very useful for studying the internal structure of automorphic forms. In this research, we investigated relationships between these invariants for automorphic forms of special kind called Aarkawa liftings. Using this result, we proposed certain conjectures on relations between invariants attached to automorphic forms on certain groups. We showed that automorphic forms called Borcherds products have strong symmetries (the multiplicative symmetries). We also studied the Borcherds products in detail in the genus two Siegel modular case. In particular, we obtained several results about the weights and characters of Borcherds products.
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