| Project/Area Number |
20540028
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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 | Rikkyo University |
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Principal Investigator |
SATO Fumihiro Rikkyo University, 理学部, 教授 (20120884)
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| Co-Investigator(Renkei-kenkyūsha) |
HIRONAKA Yumiko 早稲田大学, 教育総合科学学術院, 教授 (10153652)
KOGISO Takeyoshi 城西大学, 理学部, 准教授 (20282296)
TANIGUCHI Takashi 神戸大学, 理学研究科, 講師 (60422391)
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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 |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 数論 / 概均質ベクトル空間 / 保型超関数 / ゼータ関数 / クリフォード代数 / 関数等式 / 対称空間 |
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| Research Abstract |
Theory of prehomogeneous vector spaces gives a systematic method of constructing zeta functions from polynomial invariants of prehomogeneous group actions. We investigated zeta functions of prehomogeneous vector spaces from the following 3 view points : (1) relations to Eisenstein-periods, (2) relations to the Koecher-Maass zeta functions of automorphic forms, (3) zeta functions of invariants of non-prehomogeneous group-actions. The most important result is the construction of zeta functions of non-degenerate quadratic mappings, which include zeta functions of certain non-prehomogeneous polynomials of degree 4.
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