Updated on 2025/04/02

写真a

 
MIYAUCHI Michitaka
 
Organization
Faculty of Education Professor
Position
Professor
External link

Degree

  • Doctor of Science ( 2004.9   Kobe University )

Research Interests

  • ε-因子

  • L-因子

  • p-進代数群

Research Areas

  • Natural Science / Algebra

Education

  • Kobe University   大学院自然科学研究科 博士課程後期課程   構造化学専攻

    2001.4 - 2004.9

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Research History

  • Okayama University   Graduate School of Education   Associate Professor

    2016.4

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Professional Memberships

 

Papers

  • 仮商修正における手隠し法の取り扱いと性質について

    宮内通孝

    岡山大学算数・数学教育学会誌パピルス   30   8 - 11   2024.2

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  • A remark on conductor, depth and principal congruence subgroups Reviewed

    Michitaka Miyauchi, Takuya Yamauchi

    Journal of Algebra   592 ( 15 )   424 - 434   2022.2

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    Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

    DOI： 10.1016/j.jalgebra.2021.10.032

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  • On L-factors attached to generic representations of unramified U(2,1) Reviewed

    Michitaka Miyauchi

    Mathematische Zeitschrift   289 ( 3-4 )   1381 - 1408   2018

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  • Whittaker functions associated to newforms for GL(n) over p-adic fields Reviewed

    Miyauchi Michitaka

    Tokyo Sugaku Kaisya Zasshi   66 ( 1 )   17 - 24   2014

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    Language：English   Publisher：The Mathematical Society of Japan  

    Let F be a non-Archimedean local field of characteristic zero. Jacquet, Piatetski-Shapiro and Shalika introduced the notion of newforms for irreducible generic representations of GLn(F). In this paper, we give an explicit formula for Whittaker functions associated to newforms on the diagonal matrices in GLn(F).

    DOI： 10.2969/jmsj/06610017

    CiNii Article

    CiNii Books

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    Other Link： https://jlc.jst.go.jp/DN/JALC/10027905745?from=CiNii

  • Semisimple types for p-adic classical groups Reviewed

    Michitaka Miyauchi, Shaun Stevens

    Mathematische Annalen   358 ( 1-2 )   2014

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Research Projects

  • New developments of automorphy of Galois representations and Serre conjecture.

    Grant number：19H01778  2019.04 - 2024.03

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)  Grant-in-Aid for Scientific Research (B)

    山内 卓也, 都築 暢夫, 山名 俊介, 宮内 通孝

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    Grant amount：\15990000 （ Direct expense: \12300000 、 Indirect expense：\3690000 ）

    今年度は先ず保型性問題に必要な保型表現に関する基礎的な知識・技術等の修得、ガロア表現の保型性に必要不可欠なセール予想解決に向けて必要なテータ作用素の計算、クリスタリン表現へのリフトを計算するためのガロアコホモロジーの解析、およびガロア表現の詳細な解析を行った。さらに、GSp4の場合に保型的な法p表現の潜在的対角化可能性を示し、多くの場合のセール予想の重さの部分を解決した。
    テータ作用素に関しては、２０１４年頃に得られた自身の結果を、さらに見直すことで新しいテータサイクルを見つけ出すことに成功し、従来のものは重さに強い制限が付いていたが、一般の重さに対するテータサイクルを定義することが可能となった。ガロアコホモロジーの計算に関しては昨年ドイツ滞在中に計算したガロアコホモロジーの計算を指針として、セール重さの古典的な定義をジーゲル形式にどのように拡張するかを考察し、指標の拡張類がどのような分岐の悪さを持つかによって重さが変動することを観測した。この部分の結果は現在論文に纏めているところである。セール予想を解決する上で必要不可欠な部分は保型的な法pガロア表現が与えられた場合、保型性を保つ良い性質を満たすリフトであるp進ガロア表現の存在を示すことが重要である。この部分を示すためにガロア表現の局所的性質である潜在的対角化可能性について大域的手法を用いた解析をGSp4の場合に実行した。その際に必要な要素として、Jacquet-Langlands 対応を用いたコンパクト形式上の代数的保型形式の解析、重さ０リフトの構成、パラホリック制限を用いた保型表現の格子の存在と悪い成分における局所成分の入れ替え等がある。Jacquet-Langlands 対応は最近GSp4の場合に非常に一般の設定で確立されておりこれを援用した。この部分は現在論文に纏めている段階である。

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

    Grant number：26800022  2014.04 - 2019.03

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B)  Grant-in-Aid for Young Scientists (B)

    Miyauchi Michitaka

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    Grant amount：\3770000 （ Direct expense: \2900000 、 Indirect expense：\870000 ）

    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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  • Ramified components of automorphic representations: local theory and its application to special L-values

    Grant number：24540021  2012.04 - 2015.03

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)  Grant-in-Aid for Scientific Research (C)

    ISHIKAWA YOSHI-HIRO, TSUZUKI Masao, YASUDA Seidai, TAKANO Keiji, MIYAUCHI Michitaka

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    Grant amount：\5070000 （ Direct expense: \3900000 、 Indirect expense：\1170000 ）

    Number theory investigation usually involves quite vast area of deep mathematics, like as the Fermat Last Theolem does. The Langlands Program, which led to the settlement of FLT, has been the central strategy of arithmetic since 70s. We follow the LP to study the ramification theory of the group U(3) representations in view point of L-/ε-factors. Our approach is resorting to integralpresentations of L-function of automorphic forms, whose ramified factors give us arithmetic info. The point is to find nice Whittaker functions appearing in the ramified factor. We can successfully detect where/which the nice ones are in the case of Real/unramified U(3). As an application to the global problem, we got algebraicity result for all the critical values of twisted L-function of generic cuspidal representaions on U(3).

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  • Study onε-factor of automorphic representations and conductor of remified components

    Grant number：21540017  2009 - 2011

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)  Grant-in-Aid for Scientific Research (C)

    ISHIKAWA Yoshihiro, MORIYAMA Tomonori, YASUDA Seidai, MIYAUCHI Michitaka, TAKANO Keiji

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    Grant amount：\4420000 （ Direct expense: \3400000 、 Indirect expense：\1020000 ）

    Number theory investigation usually involves quite vast area of deep mathematics, like as the Fermat Last Theolem does. The Langlands Program, which led to the settlement of FLT, has been the central strategy of arithmetic since 70s. We follow the LP to study the ramification theory of the group U(3) representations in view point of L-/ε-factors. Our approach is resorting to integral presentations of L-function of automorphic forms, whose ramified factors give us arithmetic info. The point is to find nice Whittaker functions appearing in the ramified factor. We can successfully detect where/which the nice ones are in the case of Real/unramified U(3).

    researchmap

 

Class subject in charge

  • Secondary Education Mathematics Content Construction Ⅲ （2024academic year） Fourth semester  - 木5～6

  • Numbers and Formulas Ⅰ （2024academic year） 3rd and 4th semester  - 水1～2

  • Mathematics Ring Theory Ⅰ （2024academic year） Third semester  - 水1～2

  • Mathematics Ring Theory Ⅱ （2024academic year） Fourth semester  - 水1～2

  • Linear Algebra Ⅰ （2024academic year） 1st semester  - 木7～8

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