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Satou Lab
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A lab that explores number theory through cyclotomic fields and Bernoulli numbers.
AboutAbout the lab
Exploring number theory through cyclotomic fields and Bernoulli numbers.
Associate Professor Satou of the Foundations of Mathematical Informatics group studies algebraic number theory.
The research topic is "the theory of cyclotomic fields and the study of Bernoulli numbers." Regarding class numbers, an important concept in number theory, the page explains that for cyclotomic fields, Iwasawa theory is known as the underlying theory.
As one approach to Bernoulli numbers, the page introduces a technique called the q-analogue.
Associate Professor Satou is also interested in applying combinatorial methods to number theory, and in cryptography.
Key terms
- Cyclotomic field
- A number system formed by adjoining roots of unity to the rational numbers. It is one of the fundamental objects of study in number theory.
- Iwasawa theory
- The theory underlying the class numbers of cyclotomic fields. It continues to be developed and generalized today, and was involved in the resolution of Fermat's Last Theorem.
- q-analogue
- A technique that deals with the numbers [1]=1, [2]=1+q, … in place of 1, 2, 3, …. They return to the ordinary numbers as q→1.
ResearchResearch themes
The research topic is the theory of cyclotomic fields and the study of Bernoulli numbers. Bernoulli numbers are named as a major barrier that must be overcome for further development of Iwasawa theory.
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MembersFaculty
- Associate ProfessorJunya Satou
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Report an errorAbout 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: “Sistema de ecuaciones lineales 3x3” Floresomg / CC BY-SA 4.0 (cropped)
- The Theory of Cyclotomic Fields and Bernoulli Numbers: “JakobBernoulliSummaePotestatum” Creator:Wirkstoff / Public domain (cropped)
- Related lab (数理情報基礎論講座 吉信 康夫): “04fig-venn-002” ASpiegler / CC BY-SA 4.0 (cropped)
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