2013 Fiscal Year Final Research Report
Arithmetic invariants and automorphic L-functions for automorphic forms of several variables
| Project/Area Number |
23540033
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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) |
SUGANO Takashi 金沢大学, 理工研究域数物科学系, 教授 (30183841)
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 |
BERNHARD Heim German University of Technology (Oman), 准教授
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| Project Period (FY) |
2011 – 2013
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| Keywords | 保型形式 / 代数群 / Borcherds lift / 対称性 / テータリフト / フーリエ展開 / 保型L関数 |
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| Research Abstract |
We investigated arithmetic properties of Arakawa lifts, which are automorphic forms on the unitary group of degree two for a quaternion algebra over the rational number field constructed via theta lifting. In particular we obtained a formula for the square of the absolute value of a certain average of Fourier coefficients of an Arakawa lift in terms of special values of automorphic L-functions.
We characterize the holomorphic Borcherds lifts on orthogonal groups of quadratic forms of signature (2, n+2) in terms of the multiplicative symmetries. We also showed that a similar fact holds for Jacobi forms.
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