Cyclotomic Fields I and II

Released on by Serge Lang
preview-18

  • Cyclotomic Fields I and II Book Detail

  • Author : Serge Lang
  • Release Date : 2012-12-06
  • Publisher : Springer Science & Business Media
  • Genre : Mathematics
  • Pages : 449
  • ISBN 13 : 1461209870
  • File Size : 38,38 MB
DOWNLOAD BOOK

Cyclotomic Fields I and II by Serge Lang PDF Summary

Book Description: Kummer'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.

Disclaimer: www.yourbookbest.com does not own Cyclotomic Fields I and II books pdf, neither created or scanned. We just provide the link that is already available on the internet, public domain and in Google Drive. If any way it violates the law or has any issues, then kindly mail us via contact us page to request the removal of the link.

Cyclotomic Fields I and II

Cyclotomic Fields I and II

File Size : 13,13 MB
Total View : 5917 Views
DOWNLOAD

Kummer's work on cyclotomic fields paved the way for the development of algebraic number theory in general by Dedekind, Weber, Hensel, Hilbert, Takagi, Artin an

Introduction to Cyclotomic Fields

Introduction to Cyclotomic Fields

File Size : 7,7 MB
Total View : 7986 Views
DOWNLOAD

This text on a central area of number theory covers p-adic L-functions, class numbers, cyclotomic units, Fermat’s Last Theorem, and Iwasawa’s theory of Z_p-

Cyclotomic Fields and Zeta Values

Cyclotomic Fields and Zeta Values

File Size : 2,2 MB
Total View : 3914 Views
DOWNLOAD

Written by two leading workers in the field, this brief but elegant book presents in full detail the simplest proof of the "main conjecture" for cyclotomic fiel

Cyclotomic Fields I and II

Cyclotomic Fields I and II

File Size : 23,23 MB
Total View : 2091 Views
DOWNLOAD

Kummer's work on cyclotomic fields paved the way for the development of algebraic number theory in general by Dedekind, Weber, Hensel, Hilbert, Takagi, Artin an