Hiroki Takahashi

Profile Information

Affiliation: Professor, Graduate School of Technology, Industrial and Social Sciences, Tokushima University

Degree: Doctor(Mathematical Science)(The University of Tokyo)

Other name(s) (e.g. nickname): SUMIDA-TAKAHASHI Hiroki
J-GLOBAL ID: 200901018455233989
researchmap Member ID: 1000222380

External link: https://hiro2.pm.tokushima-u.ac.jp/~hiroki/

I am interested in complexity and uniformity of the absolute Galois group of Q. I have been studying and computing the Iwasawa invariants of cyclotomic fields. Is it possible to prove Greenberg's (generalized) conjecture? Is it possible to give a counter-example of Vandiver's conjecture, or prove it?

Research Interests

Research Areas

Natural sciences / Algebra /

Research History

Apr, 2017 - Present

Professor, Graduate School of Technology, Industrial and Social Sciences, Tokushima University
Apr, 2016 - Mar, 2017

Professor, Graduate School of Technology and Science, The University of Tokushima
Aug, 2013 - Mar, 2016

Professor, Institute of Technology and Science, The University of Tokushima
Mar, 2009 - Jul, 2013

Associate professor, Graduate School of Science, Hiroshima University
Sep, 2005 - Feb, 2009

Associate professor, Faculty of Engineering, The University of Tokushima
Oct, 1996 - Aug, 2005

Research associate, Faculty of Integrated Arts and Sciences, Hiroshima University
Oct, 2002 - Aug, 2003

Vsiting scholar, Department of Mathematics, University of Washington
Apr, 1996 - Sep, 1996

日本学術振興会特別研究員(PD)

Education

Apr, 1992 - Mar, 1996

Mathematical Sciences, Graduate School of Mathematical Sciences, The University of Tokyo
Apr, 1991 - Mar, 1992

Mathematics, Graduate School of Science, The University of Tokyo
Apr, 1989 - Mar, 1991

Department of Mathematics, Faculty of Science, The University of Tokyo
Apr, 1987 - Mar, 1989

S-1, Faculty of Arts and Sciences, The University of Tokyo

Committee Memberships

2015 - 2017

委員（非公開）, 日本数学会
2006 - 2010

日本数学会雑誌数学編集委員（非常任）

Major Papers

A generalized problem associated to the Kummer-Vandiver conjecture

Hiroki Sumida-Takahashi

Arnold Mathematical Journal, 9(3) 381-391, Sep, 2023 Peer-reviewedLead authorCorresponding author
Computation of the p-part of the ideal class group of certain real abelian fields

Hiroki Sumida-Takahashi

MATHEMATICS OF COMPUTATION, 76(258) 1059-1071, 2007 Peer-reviewedLead authorCorresponding author
Computation of the Iwasawa invariants of certain real abelian fields

H Sumida-Takahashi

JOURNAL OF NUMBER THEORY, 105(2) 235-250, Apr, 2004 Peer-reviewedLead authorCorresponding author
On the Iwasawa invariants of certain real Abelian fields

H Ichimura, H Sumida

TOHOKU MATHEMATICAL JOURNAL, 49(2) 203-215, Jun, 1997 Peer-reviewed
On the Iwasawa invariants of certain real abelian fields .2.

H Ichimura, H Sumida

INTERNATIONAL JOURNAL OF MATHEMATICS, 7(6) 721-744, Dec, 1996 Peer-reviewed

Misc.

Special elements and Iwasawa invariants of cyclotomic fields

Sumida-Takahashi Hiroki

Proceedings of the 14th Workshop on Number Theory, 1-12, Sep, 2016
The Iwasawa lambda_l-invariants in cyclotomic Z_p-extensions

Sumida-Takahashi Hiroki

Proceedings of the workshop on Number Theory 2013, 30-39, Nov, 2013
The theory of Gamma-extensions and Iwasawa main conjecture of cyclotomic fields

Sumida-Takahashi Hiroki

Proceedings of the 9th Workshop on Number Theory, 1-17, Jan, 2012
Euler's mathematics and "Letters to a German princess"

Takahashi Hiroki

Surikaisekikenkyusho Kokyuroku, 1739 203-213, Jan, 2011
Numerical errors of "Introduction to infinite analysis"

Takahashi Hiroki

Surikaisekikenkyusho Kokyuroku, 1583 168-179, Feb, 2008
Rounding around zeta values of quadratic fields and ideal calss groups of cyclotomic fields

Sumida-Takahashi Hiroki

Proceedings of the workshop on Number Theory 2007, 109-117, Jul, 2007
Numerical computation of Iwasawa invariants of cyclotomic fields and higher K-groups

Sumida-Takahashi Hiroki

Proceedings of the workshop on Number Theory 2005, 117-128, May, 2005
Special elements and locally trivial cocycles in Iwasawa Theory

Sumida-Takahashi Hiroki

Surikaisekikenkyusho Kokyuroku, 1376 20-31, 2004
Kubota-Leopold's p-adic L-function

Sumida Hiroki

Proceedings of Number Theory Summer School 9th, 117-134, 2002
Kummer generators and capitulation of ideals in Z_p-extension

Sumida Hiroki

Kenkyu Shukai Hokokushu VIII Number Theory, 61-64, Jul, 1997
Iwasawa invariants of certain real abelian fields

Sumida Hiroki, Ichimura Humio

Kenkyu Shukai Hokokushu V Number Theory, 96-102, Jul, 1996
Iwasawa $\lambda$-invariants of certain types of real abelian fields

Sumida Hiroki, Ichimura Humio

Surikaisekikenkyusho Kokyuroku, 971 78-89, 1996
On Greenberg's conjecture

Sumida Hiroki

Surikaisekikenkyusho Kokyuroku, 844 26-38, 1993

Books and Other Publications

レオナルド・デカルト・オイラー理工系数学基礎講座ＬＤＥ

高橋浩樹

現代数学社, Aug 21, 2024 (ISBN: 9784768706411)
オイラー無限解析の源流 (双書・大数学者の数学 3)

高橋浩樹

現代数学社, Feb 18, 2010 (ISBN: 9784768703878)
無限オイラー解析: Zの等式への誘い

高橋浩樹

現代数学社, Jul 7, 2007 (ISBN: 9784768703755)

Presentations

数論的特殊元と Greenberg 予想

高橋浩樹

大阪大学整数論保型形式セミナー, Oct 18, 2024
一般 Greenberg 予想と p 単数のペアリング

高橋浩樹

広島大学数学教室談話会, Sep 29, 2022
ある種の 2 ベキ次巡回拡大体のイデアル類群について

高橋浩樹

早稲田整数論セミナー, Nov 26, 2021
ゼータ値と円分体

高橋浩樹

岐阜数理科学セミナー, Jun 22, 2018
円単数・ガウス和と岩澤加群

高橋浩樹

代数的整数論研究集会（東京理科大学）, Jun 18, 2017
円分体の一般Greenberg予想とK群の特殊元

高橋浩樹

九州代数的整数論2017, Mar 10, 2017
円分体の特殊元と岩澤不変量

高橋浩樹

北陸数論研究集会, Dec 26, 2015
代数体の岩澤不変量について

高橋浩樹

愛媛大学代数セミナー, May 26, 2014
円分体の一般Greenberg予想に関するある計算法

高橋浩樹

大阪大学整数論・保型形式セミナー, May 23, 2014
The Iwasawa lambda_l invariants in cyclotomic Z_p-extensions

高橋浩樹

早稲田大学整数論研究集会, Mar 16, 2013
p 円分体の岩澤主予想

高橋浩樹

北陸数論研究集会, Dec 26, 2012
円分体の岩澤不変量の観察

高橋浩樹

九州代数的整数論 2012, Feb 23, 2012
Γ-拡大の理論と円分体の不変量

高橋浩樹

北陸数論研究集会, Dec 26, 2010

Professional Memberships

Research Projects

数論トポロジーと種々のモノドロミー不変量の新たな展開

科学研究費助成事業基盤研究(A), 基盤研究(A), 日本学術振興会, Apr, 2020 - Mar, 2025

中村博昭, 角皆宏, 河澄響矢, 森下昌紀, 星明考, 伊吹山知義, 古庄英和, 高橋浩樹, 小笠原健
Analysis of the structures of Iwasawa modules of several variables by special elements of K-groups

Grant-in-Aid for Scientific Research(C), JSPS, Apr, 2017 - Mar, 2023

Takahashi Hiroki
Analysis of the structures of Iwasawa modules by arithmetic special elements

Grant-in-Aid for Scientific Research(C), JSPS, Apr, 2013 - Mar, 2018

Takahashi Hiroki
Computational study of K3 surfaces

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, Apr, 2013 - Mar, 2016

Shimada Ichiro, Ishii Akira, Kimura Shun-ichi, Takahashi Nobuyoshi, Matsumoto Makoto, Hiranouchi Toshiro, Takahashi Hiroki
Research on the structure of Iwasawa modules for p-adic representations

Grant-in-Aid for Scientific Research(C), Grant-in-Aid for Scientific Research (C), JSPS, Apr, 2009 - Mar, 2012

Takahashi Hiroki
K3 surfaces and related algebraic varieties

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (B), Japan Society for the Promotion of Science, 2008 - 2011

SHIMADA Ichiro, KIMURA Shun-ichi, ISHII Akira, TAKAHASHI Nobuyoshi, TAKAHASHI Hiroki, SUMIHIRO Hideyasu, HIRANOUCHI Toshiro, MATSUMOTO Makoto, ITO Hiroyuki, MUTSUMI Saito, OKA Mutsuo, KONDO Shigeyuki, MATSUMOTO Keiji, TERAO Hiroaki, ISHIKAWA Goo
Hilbert-Speiser number fields and Stickelberger ideals

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, 2007 - 2010

ICHIMURA Humio
Research on Iwasawa modules for p-adic Galois representations by special elements

Grant-in-Aid for Young Scientists (B), JSPS, Apr, 2004 - Mar, 2006

Takahashi Hiroki
Study of the structure of integer rings from the view point of cyclotomic Iwasawa theory

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, 2004 - 2006

ICHIMURA Humio, NAITO Hirotada, KOYA Yoshihiro, SUMIDA Hiroki, AIBA Akira
Analysis of ideal class groups by special elements of cyclotomic fields

Grant-in-Aid for Young Scientists (B), JSPS, Apr, 2001 - Mar, 2002

Sumida Hiroki
Analysis of algebraic number fields by Gauss sums and cyclotomic units

?Grant for Japan-related Research Project, The Sumitomo Foundation, Nov, 2000 - Nov, 2001

Sumida Hiroki
Unramified extensions of algebraic number fields and special values of L-functions

Grant-in-Aid for Young Scientists (A), JSPS, Apr, 1999 - Mar, 2000

Sumida Hiroki
On the Iwasawa invariants of totally real number fields

Grant-in-Aid for Young Scientists (A), JSPS, Apr, 1997 - Mar, 1998

Sumida Hiroki