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

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.

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

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.

* 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.

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.

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.

* 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.

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.

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 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 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 ).

* 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.

Heidenstam was born in 1859, of a prosperous family.

Sherlock Holmes, the ancestor of all private eyes, was born during the 1890s.

Henrietta was discovering in the process of writing, as the born writer does, not merely a channel for the discharge of accumulated information but a stimulus to the development of the creative powers of observation, insight and intuition.

She was born Lilian Steichen, her parents immigrants from Luxemburg.

`` My mother read a book right after I was born and there was a Lilian in the book she loved and I became Lilian -- and eventually I became Paula ''.

By now she was sure she was going to have a baby, deciding it would be born in India or Burma that November.

He was born in Savannah, Georgia, in 1909.

About the only time the Hetman seemed excited was when one of his own pet ideas was born.

On April 10, 1904, his first child was born, a son named George after the late Senator.

Modern warfare was born in this campaign -- periscopes, camouflage, booby traps, land mines, extended order, trench raids, foxholes, armored cars, night attacks, flares, sharpshooters in trees, interlaced vines and treetops, which were the forerunners of barbed wire, trip wires to thwart a cavalry charge, which presaged the mine trap, and the general use of anesthetics.

Deppy is Despina Messinesi, a long-time member of the Vogue staff who, although born in Boston, was born there of Greek parents.

Samuel Gorton was born at Gorton, England, near the present city of Manchester, about 1592.

Whether the Fathers, who died before Christ was born of the Virgin Mary, were justified and saved only by the blood which he shed, and the death which he suffered after his incarnation??

Whether the only price of our redemption were not the death of Christ on the cross, with the rest of his sufferings and obediences, in the time of his life here, after he was born of the Virgin Mary??

In the judgment of Chief of Staff Scott it was ironic that the draft policy of a Democratic President, aimed at Germany, had to be pushed through the House of Representatives by the ranking minority member of the Military Affairs Committee -- a Republican Jew born in Germany!!

Thus, the Church was born and because of its intrinsic character was soon identified as a conservative institution, determined to resist the forces of change, to identify itself with the political rulers, and to maintain a kind of splendid isolation from the masses.

And she replied, `` I was born in America, but I was conceived in Vienna ''.

I was born angry.

He kept his attacks on Republicanism for partisan campaigns, but that is part of the game he was born to play.