mathematics

Haruzo Hida

Haruzo Hida 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 Haruzo Hida rather than just read about it. In short: Haruzo Hida (肥田晴三 Hida Haruzo, born 6 August 1952, Sakai, Osaka) is a Japanese mathematician, known for his research in number theory, algebraic geometry, and modular forms. Hida received from Kyoto University a B.A. in 1975, an M.A. in 1977, and a Ph.D. in 1980 with thesis On Abelian Varieties with Complex Multiplication as Factors of the Jacobians of Shimura Curves, although he left Kyoto University in 1977.

Key takeaways

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

Reference excerpt

Haruzo Hida (肥田晴三 Hida Haruzo, born 6 August 1952, Sakai, Osaka) is a Japanese mathematician, known for his research in number theory, algebraic geometry, and modular forms. Hida received from Kyoto University a B.A. in 1975, an M.A. in 1977, and a Ph.D. in 1980 with thesis On Abelian Varieties with Complex Multiplication as Factors of the Jacobians of Shimura Curves, although he left Kyoto University in 1977. He was from 1977 to 1984 an assistant professor and from 1984 to 1987 an associate professor at Hokkaidō University. Since 1987 he has been a professor at the University of California, Los Angeles. From 1979 to 1981 he was a visiting scholar at the Institute for Advanced Study. Hida was an invited speaker at the International Congress of Mathematicians (Berkeley) in 1986. In 1991 he was awarded the Guggenheim Fellowship. Hida received in 1992 for his research on p-adic L-functions of algebraic groups and p-adic Hecke rings the Spring Prize of the Mathematical Society of Japan. In 2012 he was elected a Fellow of the American Mathematical Society. He received the 2019 Leroy P. Steele Prize for Seminal Contribution to Research for his highly original paper "Galois representations into GL2( Z {\displaystyle \mathbb {Z} } p[[X]]) attached to ordinary cusp forms," published in 1986 in Inventiones Mathematicae.

Selected works Elementary theory of L-functions and Eisenstein series, Cambridge University Press, 1993 Modular forms and Galois cohomology, Cambridge University Press, 2000 Geometric modular forms and elliptic curves, World Scientific, 2000 p-Adic automorphic forms on Shimura varieties, Springer, 2004 Hilbert modular forms and Iwasawa theory, Oxford University Press, 2006

External links Homepage for Haruzo Hida at UCLA

References

Worked examples

Example 1 — a first encounter with Haruzo Hida

Start with the simplest possible case. Write down what Haruzo Hida 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 Haruzo Hida 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 Haruzo Hida 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 Haruzo Hida

In research: Haruzo Hida 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 Haruzo Hida 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: Haruzo Hida is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1952 births, 20th-century Japanese mathematicians, 21st-century Japanese mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Haruzo Hida 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 Haruzo Hida in 20 minutes

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

Frequently asked questions

What is Haruzo Hida in simple terms?

Why does Haruzo Hida 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 Haruzo Hida?

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 Haruzo Hida.