Hiroki Aoki

(青木宏樹)

Profile Information

Affiliation: Professor, Faculty of Science, Department of Mathematics, Gakushuin University

Degree: Doctor(Sience)(Kyoto University)
Master(Sience)(Kyoto University)

Contact information: aoki_hiroki_mathnifty.com
J-GLOBAL ID: 200901056166744370
researchmap Member ID: 5000055958

Research Interests

modular forms

Research Areas

Natural sciences / Algebra /

Research History

Apr, 2026 - Present

Professor, Faculty of Science, Gakushuin University
Apr, 2023 - Mar, 2026

Professor, Faculty of Science and Technology, Tokyo University of Science
Apr, 2022 - Mar, 2023

Professor, Faculty of Science and Technology, Tokyo University of Science
Apr, 2010 - Apr, 2022

Associate Professor, Faculty of Science and Technology, Tokyo University of Scienece
Apr, 2003 - Mar, 2010

Lecturer (Jr. Assoc. Prof.), Department of Science and Technology, Tokyo University of Sience

Education

Committee Memberships

Apr, 2025 - Apr, 2025

Organizers, Workshop
Jan, 2025 - Jan, 2025

Organizer, 2025 International workshop on mathematical science at TUS-Noda
Jan, 2024 - Jan, 2024

Chief Organizer, RIMS conference "Research on Automorphic forms"
Jan, 2024 - Jan, 2024

Organizer, 2024 International workshop on algebra at TUS-Noda
Jan, 2023 - Jan, 2023

Deputy representative, RIMS conference

Papers

On the upper bound of the orders of Jacobi forms

Hiroki Aoki

INTERNATIONAL JOURNAL OF MATHEMATICS, 33(8), Jun, 2022 Peer-reviewed
Generalization of the Weierstrass p function and Maass lifts of weak Jacobi forms

Hiroki Aoki

Pure and Applied Mathematics Quarterly, 16(3) 371-420, Nov, 2020 Peer-reviewed
Modular forms from the Weierstrass functions

Hiroki Aoki, Kyoji Saito

Pure and Applied Mathematics Quarterly, 16(4) 967-980, Nov, 2020 Peer-reviewedLead authorCorresponding author
The structure of mixed weight Hilbert modular forms

Hiroki Aoki, Sho Takemori

INTERNATIONAL JOURNAL OF MATHEMATICS, 30(2), Feb, 2019 Peer-reviewed
ON JACOBI FORMS OF REAL WEIGHTS AND INDICES

Hiroki Aoki

OSAKA JOURNAL OF MATHEMATICS, 54(3) 569-585, Jul, 2017 Peer-reviewed

Misc.

特集「有限群からその先へ」：「モジュラー群」

青木宏樹

数学セミナー（日本評論社）, 62(2023-3) 30-33, Feb, 2023
特集「楕円関数の味わい」：「楕円関数とヤコビ形式」

青木宏樹

数学セミナー（日本評論社）, 60(2021-10) 26-32, Sep, 2021
特集「保型形式を考えるその面白さと魅力」コラム「保型形式と微分作用素」

青木宏樹

数理科学（サイエンス社）, 692(2021-2) 46-47, Jan, 2021
書評伊吹山知義：保型形式特論（共立叢書現代数学の潮流）

青木宏樹

数学（日本数学会機関誌）, 72(1) 107-111, Jan, 2020
On mixed weight Hilbert modular forms and their structure theorem

Aoki Hiroki

数理解析研究所講究録, 2100 65-79, Jan, 2019

Books and Other Publications

特殊関数探訪（担当箇所：第５部内の「楕円関数とヤコビ形式」）

数学セミナー編集部[編]青木宏樹ほか26名[著] (Role: Joint author)

日本評論社, Sep 30, 2024 (ISBN: 9784535790193)

Presentations

101

On index-level change of Jacobi forms

Aoki Hiroki

26th Automorphic Forms Workshop, Apr 29, 2012
ヤコビ形式のインデックス - レベル変換について（坂田裕氏との共同研究）

Aoki Hiroki

2012早稲田整数論研究集会, Mar 20, 2012
On formal series of Jacobi forms and Borcherds products

Aoki Hiroki

International Workshop on Mathematics in Oman 2012, Feb 20, 2012
ヤコビ形式のインデックス - レベル変換について

Aoki Hiroki

学習院大学土曜セミナー, Dec 3, 2011
ヤコビ形式に関するいくつかの話題の紹介

Aoki Hiroki

室蘭工業大学数論セミナー, Nov 19, 2011
Borcherdsリフト

Aoki Hiroki

第１９回整数論サマースクール, Sep 7, 2011
On Jacobi Triple Product Identity and Borcherds Products

Aoki Hiroki

Seminar on automorphic forms in Tongji University, Aug 18, 2011
On the convergence of formal Fourier-Jacobi expansion

Aoki Hiroki

The 6th China-Japan Conference on number theory, Aug 15, 2011
符号のゼータ関数とリーマン予想

Aoki Hiroki

学習院大学土曜セミナー, Apr 16, 2011
無限の和と無限の積の不思議

Aoki Hiroki

第４８回「科学サロン」, Oct 4, 2010
On the Jacobi Triple Product Identity and Borcherds Products

Aoki Hiroki

Seminar Aachen-Koeln-Lille-Siegen on Automorphic Forms, Sep 29, 2010
Borcherds による Jacobi form の構成について

Aoki Hiroki

学習院大学土曜セミナー, Sep 18, 2010
A remark on Borcherds construction of Jacobi forms

Aoki Hiroki

第５回福岡数論研究集会, Aug 24, 2010
Borcherds の無限積について

Aoki Hiroki

奈良女子大学数学科談話会, Jun 10, 2010
On the image of Fourier-Jacobi expansion

Aoki Hiroki

24th Automorphic Forms Workshop, Mar 21, 2010
On the convergence of Fourier-Jacobi expansion

Aoki Hiroki

Geometry of lattices and infinite dimensional Lie algebras, Mar 17, 2010
「ヤコビの三重積公式について」（２２日）「Borcherds 無限積について（１）」（２３日）「Borcherds 無限積について（２）」（２４日）

Aoki Hiroki

熊本大学プロジェクトゼミナール「現代数学ゼミナール講演会」, Feb 22, 2010
On the Jacobi triple product

Aoki Hiroki

Seminar at IPMU (the Institute for the Physics and Mathematics of the Universe), Feb 11, 2010
Jacobi の三重積公式について

Aoki Hiroki

学習院大学土曜セミナー, Jan 29, 2010
About the convergence of formal series of Jacobi forms

Aoki Hiroki

Mathematisches Kolloquim, Uni. Siegen, Dec 7, 2009
Formal series of Jacobi forms and Maass lifts of weak Jacobi forms

Aoki Hiroki

奈良女子大学数論研究会, Nov 10, 2009
フーリエ・ヤコビ展開の収束性とボーチャーズ無限積

Aoki Hiroki

東京理科大学理工学部数学科談話会, Sep 18, 2009
Formal series of Jacobi forms

Aoki Hiroki

第１２回整数論オータムワークショップ, Sep 8, 2009
Formal series of Jacobi forms

Aoki Hiroki

第１２回整数論オータムワークショップ, Sep 8, 2009
ヤコビ形式に関する諸結果の紹介 - 保型形式の具体的な構成という観点から

Aoki Hiroki

学習院大学土曜セミナー, Jul 4, 2009
形式的なフーリエ・ヤコビ展開の収束性について

Aoki Hiroki

早稲田整数論セミナー, Jun 5, 2009
On Vector valued Siegel modular forms

Aoki Hiroki

Seminar Aachen-Koeln-Lille-Siegen on Automorphic Forms, Jun 18, 2008
Toward the determination of the structure of Hilbert-Siegel modular forms

Aoki Hiroki

Mathematisches Kolloquim, Uni. Siegen, Mar 19, 2008
Vector valued Siegel modular forms with small levels

Aoki Hiroki

保型表現・保型形式とL関数の周辺, Jan 24, 2008
保型形式のなす環の構造について

Aoki Hiroki

城西大学大学院理学研究科数学専攻講演会, Dec 17, 2007
Vector valued Siegel modular forms with small levels

Aoki Hiroki

第１０回整数論オータムワークショップ, Nov 25, 2007
実２次体上のヒルベルト保型形式のなす環の構造について

Aoki Hiroki

上智大学理工学部談話会, Jun 4, 2007
On mixed weight Hilbert modular forms

Aoki Hiroki

Jacobi forms and applications, May 10, 2007
On the ring structure of Siegel modular forms

Aoki Hiroki

NPU-TUS Bilateral Seminar, Sep 12, 2006
Hilbert 保型形式の次元の評価

Aoki Hiroki

日本数学会秋季総合文科会, Sep 19, 2005
Estimate of the dimension of Hilbert modular forms by means of differential operator

Aoki Hiroki

Automorphic forms and Zeta functions, in Memory of Tsuneo Arakawa, Sep 6, 2004
ヤコビ形式を用いた保型形式の構造決定問題への構造決定問題へのアプローチ

Aoki Hiroki

日本数学会年会, Mar 28, 2004
コンピュータは常に正しい答を出すのか数値計算入門

Aoki Hiroki

立命館大学数学コロキウム, Dec 20, 2002
Hermitian modular forms of degree 2 with respect to the imaginary quadratic field of the discriminant -3

Aoki Hiroki

Seminar at Aachen Univ, Sep 14, 2002
Practical Construction of Borcherds Product

Aoki Hiroki

第１回保型形式周辺分野スプリングコンファレンス, Feb 18, 2002
Siegel modular forms of odd weights of level 3

Aoki Hiroki

大阪大学整数論保型形式セミナー, Nov 16, 2001
Jacobi forms, Fourier-Jacobi development, and the ring structure of automorphic forms

Aoki Hiroki

Jacobi forms and applications, Sep 25, 2001
Estimating the dimension of the space of Siegel modular forms of genus 2 withe level 2 and 3

Aoki Hiroki

Japan-German seminar, Explicit Structure of Modular Forms and Zeta Functions, Sep 11, 2001
Estimation of the dimension of modular forms by using Jacobi forms

Aoki Hiroki

九州大学組合せ論セミナー, Nov 13, 2000
Estimation of the dimension of modular forms by using Jacobi forms

Aoki Hiroki

九州大学組合せ論セミナー, Nov 13, 2000
Estimation of the dimension of modular forms by using Jacobi forms

Aoki Hiroki

Codes, Lattices, Modular forms and Vertex operator algebras, Oct 2, 2000
New approach to dimension formula using Jacobi forms

Aoki Hiroki

第３回整数論オータムワークショップ, Sep 10, 2000
Estimating Siegel modular forms of genus 2 using Jacobi forms

Aoki Hiroki

保型形式ミニ研究集会, Feb 2, 2000
Jacobi 形式を用いた genus 2 の保型形式の生成元の決定について

Aoki Hiroki

京都大学数論合同セミナー, Oct 22, 1999
Automorphic forms on the expanded symmetric domain of type IV

Aoki Hiroki

保型形式とL関数の研究, Jan 25, 1999

Professional Memberships

Research Projects

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