Studies on symmetries for automorphic forms and Borcherds products
| Project/Area Number |
26400027
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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 | Kyoto Sangyo University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
NARITA Hiroaki 熊本大学, 大学院自然科学研究科, 准教授 (70433315)
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| Research Collaborator |
SUGANO Takashi 金沢大学, 理工研究域数物科学系, 教授 (30183841)
Bernhard Heim German University of Technology, 教授
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 保型形式 / 対称性 / Borcherds積 / アフィンリー環 / ヤコビ形式 / 無限積 / Kac-Moodyリー代数 / ベクトル系 / affine Lie algebra / 完全再生可能性 |
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| Outline of Final Research Achievements |
We investigated on a condition for Siegel modular forms on congruence subgroups to have infinite product expansions. We define a notion of “generalized multiplicative symmetries” for a family of automorphic forms on various levels. We furthermore show that a family of automorphic forms with infinite product expansions satisfies generalized multiplicative symmetries. We also considered a similar problem for Jacobi forms and investigated a relation between infinite product expansions and generalized multiplicative symmetries.
We show that a Siegel modular form of degree 2 of level 1 which is simultaneously anSaito-Kurokawa lift and a Borchers product is a constant multiple of the Igusa modular form.
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Report
(4 results)
Research Products
(5 results)
