Miyazaki, Takuya

写真a

Affiliation

Faculty of Science and Technology, Department of Mathematics (Yagami)

Position

Associate Professor

External Links
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Career 【 Display / hide 】

  • 1995.04
    -
    1997.09

    日本学術振興会 ,特別研究員

  • 1997.10
    -
    2000.03

    東京都立大学理学研究科数学専攻 ,助手

  • 2000.04
    -
    2004.03

    慶應義塾大学理工学部数理科学科, 専任講師

  • 2004.04
    -
    2007.03

    慶應義塾大学理工学部数理科学科, 助教授

  • 2004.09
    -
    2006.08

    理工学部広報委員会委員

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Academic Background 【 Display / hide 】

  • 1991.03

    The University of Tokyo, Faculty of Science

    University, Graduated

  • 1993.03

    Nagoya University, Graduate School, Division of Natural Science, 数学専攻

    Graduate School, Completed, Master's course

  • 1996.03

    Kyoto University, Graduate School, Division of Natural Science, 数理解析専攻

    Graduate School, Completed, Doctoral course

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Academic Degrees 【 Display / hide 】

  • 理学, Kyoto University, 1996.03

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Research Areas 【 Display / hide 】

  • Natural Science / Algebra

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Research Keywords 【 Display / hide 】

  • Automorphic representations

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Research Themes 【 Display / hide 】

  • 実解析的保型形式の構成と応用, 

    2010.01
    -
    Present

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Papers 【 Display / hide 】

  • Theta lifts to certain cohomological representations of indefinite orthogonal groups

    Miyazaki T., Saito Y.

    Research in Number Theory (Research in Number Theory)  10 ( 2 )  2024.06

    　View Summary

    Howe and Tan (Bull Am Math Soc 28:1–74, 1993) investigated a degenerate principal series representation of indefinite orthogonal groups O(b+,b-) and explicitly described its composition series. In particular it contains a unique unitarizable irreducible submodule Π, which is isomorphic to a cohomological representation. In this paper we construct orthogonal automorphic forms locally corresponding to Π as theta liftings of holomorphic Mp2(R) cusp forms by using the Borcherds’ method (Invent Math 132:491–562, 1998). We propose a special choice of Schwartz functions to define the liftings, which yields precise descriptions of their Fourier expansions.

  • On Siegel paramodular forms corresponding to skew-holomorphic Jacobi cusp forms

    Miyazaki T.

    International Journal of Mathematics (International Journal of Mathematics)  31 ( 8 )  2020

    ISSN  0129167X

    　View Summary

    © 2020 World Scientific Publishing Company. By extending arguments by Gritsenko, we construct a lifting of skew-holomorphic Jacobi cusp forms of odd weight k + 1 and index N to Siegel paramodular forms of degree 2 with L2-integrability.

  • Fourier supports of K-finite Bessel integrals on classical tube domains

    TETSUYA KOBANA, KAORU KODAIRA, MIYAZAKI TAKUYA

    International Journal of Mathematics (International Journal of Mathematics)  29 ( 4 )  2018

    Accepted,  ISSN  0129167X

    　View Summary

    © 2018 World Scientific Publishing Co. Pte Ltd. All rights reserved. Let H G/K be the symmetric tube domain associated with the Jordan algebra Hermr(F), F = R, C, or H, and X = G/P be its Shilov boundary. Also, let IGP (χ) be a degenerate principal series representation of G. Then we investigate the Bessel integrals assigned to functions in general K-types of IG P (χ). We give individual upper bounds of their supports, when IGP(χ) is reducible. We also use the upper bounds to give a partition for the set of all K-types in IGP (χ), that turns out to explain the G-module structure of IGP (χ). Thus, our results concretely realize a relationship observed by Kashiwara and Vergne [K-types and singular spectrum, in Noncommutative Harmonic analysis, Lecture Notes in Mathematics, Vol. 728 (Springer, 1979), pp. 177-200] between the Fourier supports and the asymptotic K-supports assigned to G-submodules in IGP (χ).

  • On Fourier–Jacobi expansions of real analytic Eisenstein series of degree 2

    MIYAZAKI TAKUYA

    Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 84   85 - 122 2014

    Research paper (scientific journal), Single Work, Accepted

  • On confluent hypergeometric functions and real analytic Siegel modular forms of degree 2

    MIYAZAKI TAKUYA

    数理解析研究所講究録 1871   48 - 53 2013

    Research paper (international conference proceedings), Single Work

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Papers, etc., Registered in KOARA 【 Display / hide 】

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Presentations 【 Display / hide 】

  • Siegel paramodular forms corresponding to skew-holomorphic Jacobi cusp forms

    Takuya Miyazaki

    7th Kyoto conference on automorphic forms (zoom オンライン) , 

    2020.06
    , 

    Oral presentation (invited, special), 雪江明彦

    　View Summary

    We extend Gritsenko's argument in a suitable way to construct a lift of skew-holomorphic Jacobi cusp forms to Siegel paramodular forms.

  • 指数Nの歪正則Jacobi形式に対応する2次のSiegel paramodular 形式

    宮崎琢也

    室蘭整数論セミナー (室蘭工業大学) , 

    2018.11
    , 

    Oral presentation (invited, special)

    　View Summary

    Gritsenkoは指数Nの正則Jacobi形式から種数2のSiegel　paramodular 形式を構成した。基本的にそれを踏襲する形で、指数Nの歪正則Jacobi形式からある実解析的なベクトル値paramodular 形式へのリフトに拡張した。

  • A computation of the Bessel integrals for Sp(2,R)

    MIYAZAKI TAKUYA

    2nd Kyoto conference on automorphic forms, 

    2013.06
    , 

    Oral presentation (general)

  • On confluent hypergeometric functions and real analytic Siegel Eisenstein series

    MIYAZAKI TAKUYA

    Automorphic Representations and Related Topics (Research Institute for Mathematical Sciences Kyoto University, Kyoto, JAPAN) , 

    2013.01
    , 

    Oral presentation (invited, special)

    　View Summary

    Sp(n,R)の可約退化主系列表現のK-有限ベクトルに関する、合流型超幾何関数の存在とその性質から、退化主系列表現の組成列を導出した。また特に２次の実解析的Eisenstein級数のFourier-Jacobi展開の記述を行った。

  • Mellin transforms of a residue of Siegel-Eisenstein series

    HASEGAWA YASUKO MIYAZAKI TAKUYA

    日本数学会2007年度年会 (埼玉大学) , 

    2007
    , 

    Oral presentation (general)

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Courses Taught 【 Display / hide 】

  • BACHELOR'S THESIS

    2024

  • COMPLEX ANALYSIS 1 AND EXERCISE

    2024

  • MATHEMATICS 1B

    2024

  • MATHEMATICS 1A

    2024

  • INDEPENDENT STUDY ON FUNDAMENTAL SCIENCE AND TECHNOLOGY

    2024

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Courses Previously Taught 【 Display / hide 】

  • 数学１A

    Keio University

    2016.04
    -
    2017.03
    , 

    Spring Semester, Lecture, Within own ｆaculty, 78people

  • 代数学基礎同演習

    Keio University

    2016.04
    -
    2017.03
    , 

    Autumn Semester, Lecture, Within own ｆaculty

  • 数学１B

    Keio University

    2016.04
    -
    2017.03
    , 

    Autumn Semester, Lecture, Within own ｆaculty

  • 関数論第２

    Keio University

    2016.04
    -
    2017.03
    , 

    Spring Semester, Lecture, Within own ｆaculty

  • 数学１B

    Keio University

    2015.04
    -
    2016.03
    , 

    Autumn Semester

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Memberships in Academic Societies 【 Display / hide 】

  • 日本数学会

    　

  • American Mathematical Society

    　
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