mathematics

Hideo Shimizu

Hideo Shimizu 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 Hideo Shimizu rather than just read about it. In short: Hideo Shimizu (清水英男) (fl. 1963) is a Japanese mathematician who introduced Shimizu L-functions. References Atiyah, Michael Francis; Donnelly, H.; Singer, I.

Key takeaways

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

Reference excerpt

Hideo Shimizu (清水英男) (fl. 1963) is a Japanese mathematician who introduced Shimizu L-functions.

References Atiyah, Michael Francis; Donnelly, H.; Singer, I. M. (1982), "Geometry and analysis of Shimizu L-functions", Proceedings of the National Academy of Sciences of the United States of America, 79 (18): 5751, Bibcode:1982PNAS...79.5751A, doi:10.1073/pnas.79.18.5751, ISSN 0027-8424, JSTOR 12685, MR 0674920, PMC 346984, PMID 16593231 Atiyah, Michael Francis; Donnelly, H.; Singer, I. M. (1983), "Eta invariants, signature defects of cusps, and values of L-functions", Annals of Mathematics, Second Series, 118 (1): 131–177, doi:10.2307/2006957, ISSN 0003-486X, JSTOR 2006957, MR 0707164 Shimizu, Hideo (1963), "On discontinuous groups operating on the product of the upper half planes", Annals of Mathematics, Second Series, 77 (1): 33–71, doi:10.2307/1970201, ISSN 0003-486X, JSTOR 1970201, MR 0145106

Worked examples

Example 1 — a first encounter with Hideo Shimizu

Start with the simplest possible case. Write down what Hideo Shimizu 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 Hideo Shimizu 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 Hideo Shimizu 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 Hideo Shimizu

In research: Hideo Shimizu 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 Hideo Shimizu 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: Hideo Shimizu is common in secondary-school and first-year university syllabi. It links to neighbouring topics 20th-century Japanese mathematicians, Asian mathematician stubs, Living people, so understanding it makes those chapters shorter.
In everyday life: Look for Hideo Shimizu 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 Hideo Shimizu in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Hideo Shimizu 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 Hideo Shimizu out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Hideo Shimizu in simple terms?

Hideo Shimizu (清水英男) (fl. 1963) is a Japanese mathematician who introduced Shimizu L-functions. References Atiyah, Michael Francis; Donnelly, H.; Singer, I.

Why does Hideo Shimizu 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 Hideo Shimizu?

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 Hideo Shimizu.