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

Primes in the interval [kx; (k + 1)x]

Aoki Hiroki

Workshop on Jacobi Forms and Number Theory, Jul 17, 2025
Root systems and in nite product

Aoki Hiroki

2025 International Conference on Number Theory and Modular Forms, Jul 15, 2025
ボーチャーズのベクトル系とルート系

Aoki Hiroki

研究集会「楕円周期積分の広がり」, Apr 5, 2025
無限積によるヤコビ形式の構成とルート系

Aoki Hiroki

第４回仙台保型形式小集会, Feb 9, 2025
「無限積＝無限和」型の等式とある種のルート系の特徴づけ

青木宏樹

数論合同セミナー, Jan 24, 2025
Generalization of Jacobi Triple Product Identity and Root Systems

Aoki Hiroki

Commutative Algebra & Differential Equations, Mar 14, 2024
「無限積＝無限和」型の公式と保型形式（第２話）

Aoki Hiroki

2023大分宮崎整数論研究集会, Sep 15, 2023
Infinite products and infinite sums on modular forms

Aoki Hiroki

Workshop : Algebraicity Problems in Geometry, Analysis, and Number Theory, Apr 4, 2023
ヤコビ形式の消滅次数について

Aoki Hiroki

第１回仙台保型形式小集会2022, Jan 22, 2022
ワイエルシュトラスの楕円関数から導かれる保型形式について（齋藤恭司氏との共同研究）

Aoki Hiroki

2020大分整数論研究集会, Oct 10, 2020
Formal series of Jacobi forms

Aoki Hiroki

Oberseminar Institut fuer Algebraische Geometrie, Leibniz Universitaet Hannover, Mar 12, 2020
ヤコビ形式の理論と応用

Aoki Hiroki

東北大学数理科学連携研究センターと東京理科大学総合研究院の連携研究協定ミーティング, Mar 4, 2020
数学者が見ている数の世界

Aoki Hiroki

「サイエンス夢工房」公開講座, Dec 14, 2019
「無限積＝無限和」型の公式と保型形式

Aoki Hiroki

第１回大分数論研究集会, Aug 5, 2019
A short survey on elliptic modular forms (part of `Elliptic Artin groups II')

Aoki Hiroki

IPMU Special Seminar `Elliptic Artin groups I, II', Mar 31, 2019
On Maass lifts of weak Jacobi forms

Aoki Hiroki

Seminar on automorphic forms in Mannheim University, Jan 17, 2019
ワイエルシュトラスのペー関数の一般化と弱ヤコビ形式のマースリフトについて

Aoki Hiroki

2018大分鹿児島整数論研究集会, Oct 6, 2018
弱ヤコビ形式のマースリフトについて

Aoki Hiroki

京都大学数論合同セミナー, May 18, 2018
混合重みヒルベルト保型形式の構成と全体構造の決定について

Aoki Hiroki

Automorphic forms/representaions on covering groups, Mar 22, 2018
On the structures of mixed weight Hilbert modular forms on real quadratic fields

Aoki Hiroki

Workshop On Jacobi Forms and Applications, Mar 14, 2018
On mixed weight Hilbert modular forms and their structure theorem

Aoki Hiroki

保型形式の解析的・数論的研究, Jan 16, 2018
On the structure of mixed weight Hilbert modular forms

Aoki Hiroki

Seminar Aachen-Bonn-Koeln-Lille-Siegen on Automorphic Forms, Nov 22, 2017
ヤコビ形式の簡単な紹介

Aoki Hiroki

神楽坂代数セミナー, Jun 27, 2017
簡単な代数学の知識だけで進むヒルベルト保型形式の話

Aoki Hiroki

九大代数学セミナー, Jun 16, 2017
On the structure theorem for modular forms ... Igusa’s result and beyond

Aoki Hiroki

Local zeta functions and the arithmetic of moduli spaces: A conference in memory of Jun-Ichi Igusa, Mar 25, 2017
A remark on the structure of mixed weight Hilbert modular forms

Aoki Hiroki

Seminar on automorphic forms in Mannheim University, Dec 1, 2016
On the structure of Hilbert modular forms with discriminant 5

Aoki Hiroki

Oberseminar Modulfunktionen (in Heidelberg University), Nov 30, 2016
ヤコビの三重積を保型形式の立場から見てみる

Aoki Hiroki

新潟代数セミナー, Oct 25, 2016
ヤコビ形式の無限積表示について

Aoki Hiroki

愛知数論セミナー, Oct 22, 2016
実数重み、実数指数のヤコビ形式について

Aoki Hiroki

大阪大学整数論保型形式セミナー, Oct 14, 2016
A remark on the weights of Siegel modular forms

Aoki Hiroki

30th Automorphic Forms Workshop, Mar 10, 2016
A remark on the weights of modular forms

Aoki Hiroki

Seminar on automorphic forms in Mannheim University, Dec 21, 2015
分数重み、分数指数のヤコビ形式について

Aoki Hiroki

香川セミナー, Jul 11, 2015
「無限積＝無限和」の等式を与えるヤコビ形式について

Aoki Hiroki

東北大学組合せ論セミナー, Mar 17, 2015
On Jacobi forms which connect infinite products and infinite sums

Aoki Hiroki

Representations, Vertex Operator Algebras, and Algebraic Combinatorics, Dec 17, 2014
Structure theorem of the space of automorphic forms of several variables

Aoki Hiroki

第１７回整数論オータムワークショップ, Nov 6, 2014
Estimation of the dimension of modular forms of several variables

Aoki Hiroki

Oberseminar Modulfunktionen (in Heidelberg University), Aug 21, 2014
On the structure of mixed weight Hilbert modular forms

Aoki Hiroki

Seminar on automorphic forms in Mannheim University, Aug 19, 2014
On Jacobi forms of rational weight and rational index

Aoki Hiroki

28th Automorphic Forms Workshop, May 15, 2014
Some Problems on Jacobi Forms

Aoki Hiroki

Seminar on automorphic forms in Tongji University, Apr 1, 2014
Jacobi forms of rational weight and rational index

Aoki Hiroki

Explicit Theory of Automorphic Forms, Mar 25, 2014
Determination of the structure of vector valued Siegel modular forms by using Jacobi forms

Aoki Hiroki

2014早稲田整数論研究集会, Mar 12, 2014
Determination of the structure of vector valued Siegel modular forms by using Jacobi forms

Aoki Hiroki

2014早稲田整数論研究集会, Mar 12, 2014
On Jacobi forms of fractional weight

Aoki Hiroki

The 7th China-Japan Conference on number theory, Oct 31, 2013
On Maass lift to Siegel paramodular forms

Aoki Hiroki

Workshop on Modular Forms and Jacobi Forms, Jun 12, 2013
On Siegel paramodular forms of degree 2 with small levels

Aoki Hiroki

27th Automorphic Forms Workshop, Mar 11, 2013
On modular forms of the Siegel paramodular group

Aoki Hiroki

Workshop on Modular Forms, Sep 29, 2012
ジーゲルパラモジュラー保型形式について

Aoki Hiroki

学習院大学土曜セミナー, Sep 15, 2012
Borcherds による無限積をもちいたヤコビ形式の構成について

Aoki Hiroki

KSU整数論セミナー, Jul 13, 2012
ヤコビ形式のインデックス - レベル変換について（その２）（坂田裕氏との共同研究）

Aoki Hiroki

早稲田整数論セミナー, Jun 8, 2012

Professional Memberships

Research Projects

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