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Institute of Science Tokyo

Undergraduate: School of Science, Department of Mathematics

Graduate: School of Science, Mathematics Course

鈴木研究室

Showing the original Japanese · View translation

ゼータ関数やL関数を解析の手法で調べる、解析数論の研究室。

Analytic number theoryZeta functionsL-functions

リーマン・ゼータ関数の値を複素平面上の色で表した図 — *Illustrative image. Not taken at the lab.

AboutAbout the lab

ゼータ関数を、解析の目で調べる。

鈴木研究室は、数論のなかでも、ゼータ関数やL関数の性質を調べる解析数論を研究しています。
古典的なゼータ関数のほか、数論的スキームや代数群のゼータ関数も研究の対象です。
ゼータ関数と、数論幾何や表現論、関数解析、偏微分方程式など、ほかの分野とのつながりにも取り組んでいます。
指導した修士論文には、素数の分布や分割数、ゼータ関数の零点など、さまざまなテーマがあります。

Key terms

解析数論: 微分や積分など解析学の方法を使って、素数の分布など整数の性質を調べる数論の分野
ゼータ関数: 素数や整数の情報を映し出す特別な関数。代表例はリーマン・ゼータ関数
L関数: ゼータ関数を一般にしたもの。数論に出てくるさまざまな対象ごとに作られる

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ResearchResearch themes

*Illustrative image

ゼータ関数の「ねじ関数」

素数の分布の謎を秘めたリーマンゼータ関数に対応する「ねじ関数」という関数を調べています。その性質を使って、ゼータ関数の零点の位置や、偶数を2つの素数の和で表すゴールドバッハ問題に迫ります。

リーマン予想と確率の分布

数学最大の難問の一つ、リーマン予想は、確率論の言葉で言い換えられることがあります。予想と結びつく「無限分解可能」な確率分布を調べ、数論と確率論の間の新しいつながりを探っています。

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Professor鈴木正俊Publications ↗

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Immersed in researchPlenty of free time

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About the images

The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).

Top image: “Complex zeta” Jan Homann / Public domain (cropped)
ゼータ関数の「ねじ関数」: “Goldbach 3” Fournier Paul / CC0 (cropped)
Related lab (プルカイト研究室): “J-inv-phase” Linas Vepstas / CC BY-SA 3.0 (cropped)
Related lab (利根川研究室): “Minimalfläche mit Seifenhaut Würfel 0328” Bin im Garten / CC BY-SA 3.0 (cropped)
Related lab (田口研究室): “Ulam spiral with prime numbers and divisor-based dot sizes” Marianoju / CC BY-SA 4.0 (cropped)
Related lab (谷田川研究室): “Riemann surface sqrt” Jan Homann / Public domain (cropped)

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