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.

* 1962 Kenkichi Iwasawa, Bernard M. Dwork

Kenkichi Iwasawa ( Iwasawa Kenkichi, September 11, 1917 – October 26, 1998 ) was a Japanese mathematician who is known for his influence on algebraic number theory.

* 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.

On the Iwasawa algebra associated to a normal element of Cp, Proc.

* In Japan, according to M. Iwasawa at the National Institute of Population and Social Security Research, less than 3 % of females between 25-29 are currently cohabiting, but more than 1 in 5 have had some experience of an unmarried partnership, including cohabitation.

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.

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.

* Iwasawa decomposition ( KAN ) a mathematical process dealing with Lie groups

Before that he worked on Lie groups and Lie algebras, introducing the general Iwasawa decomposition.

A more recent Iwasawa study has shown that there has been a recent emergence of non-marital cohabitation.

In the last ten years he has focused on the study of various aspects of non-commutative Iwasawa theory, for instance, the study of the arithmetic of elliptic curves in nonabelian infinite extensions.

* Iwasawa Yoshihiko 岩沢愿彥.

Also, starting with any compact real form of a semisimple Lie algebra g its complexification as a real Lie algebra of twice the dimension splits into g and a certain solvable Lie algebra ( the Iwasawa decomposition ), and this provides a canonical bicrossproduct quantum group associated to g. For su ( 2 ) one obtains a quantum group deformation of the Euclidean group E ( 3 ) of motions in 3 dimensions.

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

In the early 1970s, Barry Mazur considered generalizations of Iwasawa theory to abelian varieties.

More recently ( early 90s ), Ralph Greenberg has proposed an Iwasawa theory for motives.

Iwasawa studied classical Galois modules over by asking questions about the structure of modules over.

More generally, Iwasawa theory asks questions about the structure of Galois modules over extensions with Galois group a p-adic Lie group.

In order to get an interesting Galois module here, Iwasawa took the ideal class group of, and let be its p-torsion part.

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

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.

* Greenberg, Ralph, Iwasawa Theory-Past & Present, Advanced Studies in Pure Math.

Combining this with the p-parity theorem by and the announced proof of the main conjecture of Iwasawa theory for GL ( 2 ) by, they conclude that a positive proportion of elliptic curves over Q have analytic rank zero, and hence, by, satisfy the Birch and Swinnerton-Dyer conjecture.

* Borel, A .; Chowla, S .; Herz, C. S .; Iwasawa, K .; Serre, J .- P. Seminar on complex multiplication.

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

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.

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.

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.

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.

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

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.

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

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.

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.

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

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