| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2019: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2018: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Outline of Final Research Achievements |
We investigated on relations between certain symmetries of automorphic forms of several variables and infinite product expansions of Borcherds type. Our goal is to show that a family of automorphic forms with multiplicative symmetries of level structure has an infinite product expansion of Borcherds type. In this study, we showed that a family of Jacobi forms with multiplicative symmetries of level structure has an infinite product expansion. By using this result, we also showed that a family of Siegel modular forms of degree 2 with multiplicative symmetries of level structure has an infinite product expansion. We also proved that a plane curve with a single symmetry of Hecke type is in fact a modular curve, and that completely replicable functions are characterized by multiplicative symmetries of level structure.
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