Via the theory of zeta integrals initiated by Kenkichi Iwasawa and by John Tate in Tate's thesis it is related to the study of the zeta function of global fields.

Tate's thesis ( 1950 ) on Fourier analysis in number fields has become one of the ingredients for the modern theory of automorphic forms and their L-functions, notably by its use of the adele ring, its self-duality and harmonic analysis on it ; independently and a little earlier, Kenkichi Iwasawa obtained a similar theory.

The latter was explicitly introduced in papers of Kenkichi Iwasawa and John Tate.

It began as a Galois module theory of ideal class groups, initiated by Kenkichi Iwasawa, in the 1950s, as part of the theory of cyclotomic fields.

It is named after Kenkichi Iwasawa, the Japanese mathematician who developed this method.

* Iwasawa, Kenkichi: On some types of topological groups.

* 1962 Kenkichi Iwasawa, Bernard M. Dwork

* Lectures on p-adic L-functions / by Kenkichi Iwasawa ( 1972 )

* Local class field theory / Kenkichi Iwasawa ( 1986 ) ISBN 0-19-504030-9

* Algebraic functions / Kenkichi Iwasawa ; translated by Goro Kato ( 1993 ) ISBN 0-8218-4595-0

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* Kenkichi Iwasawa ( 1917 – 1998 ) Mathematician

He received Ph. D. in Mathematics at MIT in 1956 under direction of Kenkichi Iwasawa.

* Kenkichi Ueda ( 6 March 1936 – 7 September 1939 )

* Kenkichi Kataoka ( 1902 – 1904 ) Speaker of the House of Representatives ; the Lower House Speaker.

The news was compiled by NHK Nisei staffers Kenkichi Oki and George Mitsushio, but the POWs tried to subvert the propaganda wherever possible by reading it with a joking tone or by rushing through objectionable items.

George Mitsushio was News Analysis Section chief, with Kenkichi Oki in charge of the actual broadcasts, which were mostly propaganda with the notable exception of Iva Toguri's " Orphan Ann " segment.

Just after the noon unofficial meeting was held in the Palace by Araki, Mazaki, Hayashi, and also other members of the Supreme War Council Abe Nobuyuki, Ueda Kenkichi, Terauchi Hisaichi, Nishi Giichi, Prince Asaka Yasuhiko, Prince Nashimoto Morimasa, and Prince Higashikuni Naruhiko.

The Sonogashira cross-coupling reaction was first reported by Kenkichi Sonogashira, Yasuo Tohda, and Nobue Hagihara in their 1975 publication.

It also seriously injured Kenkichi Ueda, Division 9 commander of the Japanese Imperial Army,, Japanese Consul-General in Shanghai, and Shigemitsu Mamoru, Japanese Envoy in Shanghai.

In 1976, an investigation by Chicago Tribune reporter Ron Yates discovered that Kenkichi Oki and George Mitsushio, who had given the most damaging testimony at Toguri's trial, had perjured themselves.

Childhood friend Kenkichi Yabe ( Hiroshi Nihonyanagi ), a doctor, and widower, is father to a young daughter.

Iva, Cousens and Ince never worked Sundays ; Ruth Hayakawa substituted for Iva and Lieutenant Reyes substituted for Cousens and Ince under the supervision of Kenkichi Oki.

Critical interpretation of Bashō's poems continued into the 20th century, with notable works by Yamamoto Kenkichi, Imoto Nōichi, and Ogata Tsutomu.

But when Yabe's mother Tami ( Haruko Sugimura ) impulsively asks Noriko to marry Kenkichi and follow them in their northward resettlement, Noriko agrees.

Noriko's parents console themselves that Noriko and Kenkichi will move back to Tokyo in a few years ' time, and the family will be reunited.

From left: Nagaoka Kenkichi, Mizobuchi Hironojō, Sakamoto Ryōma, Yamamoto Kōdō, Sugano Kakubei, Shiramine Shunme.

* Mathematics: Approximation theory — Arakelov theory — Asymptotic theory — Bifurcation theory — Catastrophe theory — Category theory — Chaos theory — Choquet theory — Coding theory — Combinatorial game theory — Computability theory — Computational complexity theory — Deformation theory — Dimension theory — Ergodic theory — Field theory — Galois theory — Game theory — Graph theory — Group theory — Hodge theory — Homology theory — Homotopy theory — Ideal theory — Intersection theory — Invariant theory — Iwasawa theory — K-theory — KK-theory — Knot theory — L-theory — Lie theory — Littlewood – Paley theory — Matrix theory — Measure theory — Model theory — Morse theory — Nevanlinna theory — Number theory — Obstruction theory — Operator theory — PCF theory — Perturbation theory — Potential theory — Probability theory — Ramsey theory — Rational choice theory — Representation theory — Ring theory — Set theory — Shape theory — Small cancellation theory — Spectral theory — Stability theory — Stable theory — Sturm – Liouville theory — Twistor theory

* The Iwasawa decomposition G = KAN of a semisimple group G as the product of compact, abelian, and nilpotent subgroups generalises the way a square real matrix can be written as a product of an orthogonal matrix and an upper triangular matrix ( a consequence of Gram – Schmidt orthogonalization ).

The main conjecture of Iwasawa theory was formulated as an assertion that two methods of defining p-adic L-functions ( by module theory, by interpolation ) should coincide, as far as that was well-defined.

At that time, Kitagawa was eating a Yuzu sherbet, so he named the band after the fruit ( incidentally, Iwasawa was eating vanilla ice cream.

Iwasawa was born in Shinshuku-mura, a town near Kiryū, in Gunma Prefecture.

However, this same year Iwasawa became sick with pleurisy, and was unable to return to his position at the university until April 1947.

In 1950, Iwasawa was invited to Cambridge, Massachusetts to give a lecture at the International Congress of Mathematicians on his method to study Dedekind zeta functions using integration over ideles and duality of adeles ; this method was also independently obtained by John Tate and it is sometimes called Tate's thesis or the Iwasawa-Tate theory.

Iwasawa spent the next two years at Institute for Advanced Study in Princeton, and in Spring of 1952 was offered a job at the Massachusetts Institute of Technology, where he worked until 1967.

These elements — named Beilinson elements after Alexander Beilinson who introduced them in — were used by Kazuya Kato in to prove one divisibility in Barry Mazur's main conjecture of Iwasawa theory for elliptic curves.

In number theory, Iwasawa theory is the study of objects of arithmetic interest over infinite towers of number fields.

Iwasawa worked with so-called-extensions: infinite extensions of a number field with Galois group isomorphic to the additive group of p-adic integers for some prime p. Every closed subgroup of is of the form, so by Galois theory, a-extension is the same thing as a tower of fields such that.

In fact, is a module over the Iwasawa algebra ( i. e. the completed group ring of over ).

This idea is much used in Iwasawa theory.

Ribet's methods were pushed further by Barry Mazur and Andrew Wiles in order to prove the Main Conjecture of Iwasawa theory ,< ref > a corollary of which is a strengthening of the Herbrand-Ribet theorem: the power of p dividing B < sub > p − n </ sub > is exactly the power of p dividing the order of G < sub > n </ sub >.

Then the Iwasawa decomposition of is

and the Iwasawa decomposition of G is

Iwasawa decompositions also hold for some disconnected semisimple groups G, where K becomes a ( disconnected ) maximal compact subgroup provided the center of G is finite.

For a general semisimple Lie group, the decomposition is the Iwasawa decomposition of G as G = KAN in which K occurs in a product with a contractible subgroup AN.

Iwasawa is perhaps best known for introducing what is now called Iwasawa theory, which developed from researches on cyclotomic fields from the later parts of the 1950s.