mathematics

Tomio Kubota

Tomio Kubota is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Tomio Kubota rather than just read about it. In short: Tomio Kubota (久保田富雄, Kubota Tomio) (6 December 1930 – 30 June 2020) was a Japanese mathematician working in number theory. His contributions include works on p-adic L functions and real-analytic automorphic forms.

Key takeaways

Tomio Kubota belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Tomio Kubota to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Tomio Kubota from memory before moving on to harder problems.

Reference excerpt

Tomio Kubota (久保田富雄, Kubota Tomio) (6 December 1930 – 30 June 2020) was a Japanese mathematician working in number theory. His contributions include works on p-adic L functions and real-analytic automorphic forms. His work on p-adic L-functions, later recognised as an aspect of Iwasawa theory, was done jointly with Leopoldt. He extended the concept of metaplectic group, in a way significant for arithmetic applications. This opened a field for later research on associated Dirichlet series and automorphic forms, and was a major step in the solution of Kummer's conjecture.

Works On automorphic functions and the reciprocity law in a number field. Kinokuniya, Tokyo 1969 Notes on analytic theory of numbers. University of Chicago Press, 1963 with Sigekatu Kuroda: 整数論 : 代数的整数論の基礎. ("Number Theory. Foundations of Algebraic Number Theory"), Asakura Shoten, Tokyo 1963 Some arithmetical applications of an elliptic function, Journal für Reine und Angewandte Mathematik, Band 214/215, 1964/1965, 141-145 Kubota, T.; Leopoldt, H.-W. (1964). "Eine p-adische Theorie der Zetawerte I: Einführung der p-adischen Dirichletschen L-Funktionen". Journal für die Reine und Angewandte Mathematik. 214/215: 328–339. Kubota, Tomio (1973). Elementary theory of Eisenstein series. Kodansha, Tokyo / Wiley, New York. ISBN 978-0470509203. editor: Investigations in number theory. Academic Press, 1988

Notes

External links 1. Topological Linear Groupの被覆群 (代数的整数論研究会報告集)---名古屋大学理学部　久保田富雄　(KUBOTA, TOMIO) / Proceeding of the Conference on Algebraic Number Theory

Worked examples

Example 1 — a first encounter with Tomio Kubota

Start with the simplest possible case. Write down what Tomio Kubota claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Tomio Kubota before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Tomio Kubota ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Tomio Kubota

In research: Tomio Kubota appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Tomio Kubota in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Tomio Kubota is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1930 births, 2020 deaths, 20th-century Japanese mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Tomio Kubota outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Tomio Kubota in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Tomio Kubota means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Tomio Kubota out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Tomio Kubota in simple terms?

Why does Tomio Kubota matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Tomio Kubota?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Tomio Kubota.