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L and epsilon factors of unitary groups over a p-adic field

Research Project

Project/Area Number 26800022
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Algebra
Research InstitutionOkayama University (2016-2018)
Osaka Prefecture University (2014-2015)

Principal Investigator

Miyauchi Michitaka  岡山大学, 教育学研究科, 准教授 (70533644)

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)
KeywordsL-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).

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。

Report

(6 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Research-status Report
  • 2016 Research-status Report
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (3 results)

All 2018 2015

All Journal Article (1 results) (of which Peer Reviewed: 1 results) Presentation (2 results)

  • [Journal Article] On L-factors attached to generic representations of unramified U(2,1)2018

    • Author(s)
      Michitaka Miyauchi
    • Journal Title

      Mathematische Zeitschrift

      Volume: 印刷中 Pages: 1-28

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Presentation] Newforms for ramified U(2,1)2015

    • Author(s)
      宮内通孝
    • Organizer
      保型形式リトリート討論会
    • Place of Presentation
      セミナーカルチャーセンター臨湖(滋賀県長浜市)
    • Year and Date
      2015-09-03
    • Related Report
      2015 Research-status Report
  • [Presentation] Newforms for ramified U(2,1)2015

    • Author(s)
      宮内通孝
    • Organizer
      神戸整数論ミニ集会
    • Place of Presentation
      神戸大学大学院理学研究科(兵庫県神戸市)
    • Year and Date
      2015-05-21
    • Related Report
      2015 Research-status Report

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Published: 2014-04-04   Modified: 2020-03-30  

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