000			02390nam a2200325Ia 4500
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020			_a9781461269724 (pbk.) _c€ 59.99
040			_bENG _cIISER-BPR
041			_aENG
082			_a512.3 _bLAN _223rd
100			_aLang, Serge _91069
222			_aMathematics
245		0	_aCyclotomic fields I and II
250			_a2nd ed.
260			_aNew York: _bSpringer Science, _cc1990.
300			_axvii, 433p. : _bill. ; _c24cm
440			_aGraduate Texts in Mathematics _vVol. 121 _92550
504			_aIncludes appendices, bibliographic references and subject index.
520			_aKummer's work on cyclotomic fields paved the way for the development of algebraic number theory in general by Dedekind, Weber, Hensel, Hilbert, Takagi, Artin and others. However, the success of this general theory has tended to obscure special facts proved by Kummer about cyclotomic fields which lie deeper than the general theory. For a long period in the 20th century this aspect of Kummer's work seems to have been largely forgotten, except for a few papers, among which are those by Pollaczek [Po], Artin-Hasse [A-H] and Vandiver [Va]. In the mid 1950's, the theory of cyclotomic fields was taken up again by Iwasawa and Leopoldt. Iwasawa viewed cyclotomic fields as being analogues for number fields of the constant field extensions of algebraic geometry, and wrote a great sequence of papers investigating towers of cyclotomic fields, and more generally, Galois extensions of number fields whose Galois group is isomorphic to the additive group of p-adic integers. Leopoldt concentrated on a fixed cyclotomic field, and established various p-adic analogues of the classical complex analytic class number formulas. In particular, this led him to introduce, with Kubota, p-adic analogues of the complex L-functions attached to cyclotomic extensions of the rationals. Finally, in the late 1960's, Iwasawa [Iw 11] made the fundamental discovery that there was a close connection between his work on towers of cyclotomic fields and these p-adic L-functions of Leopoldt - Kubota.
650			_aMathematics _92551
650			_aAlgebra _92552
650			_aNumber theory _92553
650			_aCyclotomic fields _92554
942			_cBK _2ddc
942			_2ddc
947			_a5498.083500000001
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999			_c4209 _d4209