L and epsilon factors of unitary groups over a p-adic field
Project/Area Number |
26800022
|
Research Category |
Grant-in-Aid for Young Scientists (B)
|
Allocation Type | Multi-year Fund |
Research Field |
Algebra
|
Research Institution | Okayama University (2016-2018) Osaka Prefecture University (2014-2015) |
Principal Investigator |
|
Project Period (FY) |
2014-04-01 – 2019-03-31
|
Project Status |
Completed (Fiscal Year 2018)
|
Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
|
Keywords | L-因子 / ε-因子 / L関数 / ε因子 / ユニタリ群 |
Outline of Final Research Achievements |
We establish a theory of newforms for supercuspidal representations of ramified U(2,1) over a non-archimedean local field. We prove that the space of newforms for such a representation is one-dimensional, and that zeta integrals of newforms attain L-factors. We compute Rankin-Selberg L-factors of level zero, supercuspidal representations of U(2,1).
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Academic Significance and Societal Importance of the Research Achievements |
整数論における主要な研究対象のひとつに保型表現がある。局所ニューフォームは保型表現を調べるのに非常に有効な道具であるが、今のところいくつかの群についてしか見つかっていない。本研究はこれまでに私が導入し整備した不分岐U(2,1)のニューフォーム理論を、分岐群の場合に拡張したものである。この結果は将来保型表現への応用を考える上で必要不可欠なものである。
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Report
(6 results)
Research Products
(3 results)