2013 Fiscal Year Final Research Report
Lifting for Siegel modular forms of half-integral weight
| Project/Area Number |
23740018
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Joetsu University of Education (2012-2013)
Osaka University (2011) |
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Principal Investigator |
HAYASHIDA SHUICHI 上越教育大学, 学校教育研究科(研究院), 准教授 (80597766)
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| Project Period (FY) |
2011 – 2013
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| Keywords | ジーゲル・アイゼンシュタイン級数 / マース関係式 / 重さ半整数の保型形式 / リフティング / Zharkovskaya's theorem |
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| Research Abstract |
Modular forms are functions of complex variables which have nice transformation formula. So-called "liftings" are certain maps between the space of modular forms of several variables and "liftings" are useful to investigate the structure of the space of modular forms and the properties of the L-functions.
In this study I obtained lifting maps from two elliptic modular forms to Siegel modular forms of half-integral weight of even degrees under the assumption that the constructed form does not vanish. To show the lifting I obtained a certain generalization of the Maass relation for Siegel modular forms of half-integral weight of even degrees.
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