| 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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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2010: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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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 / Borcherdsリフト / 積対称性 / 四元数環 / テータリフト / 国際研究者交流 / オマーン / ジーゲル・テータ級数 / ヒルベルトモジュラー形式 / Borcherds積 / ヘッケ作用素 |
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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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