• Sign In / Register
  • Help
  • Basket0
Cyclotomic Fields I and II - Graduate Texts in Mathematics 121 (Paperback)
  • Cyclotomic Fields I and II - Graduate Texts in Mathematics 121 (Paperback)
zoom

Cyclotomic Fields I and II - Graduate Texts in Mathematics 121 (Paperback)

(assisted by), (author)
£54.99
Paperback 436 Pages / Published: 30/09/2012
  • We can order this

Usually despatched within 3 weeks

  • This item has been added to your basket
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.

Publisher: Springer-Verlag New York Inc.
ISBN: 9781461269724
Number of pages: 436
Weight: 700 g
Dimensions: 235 x 155 x 23 mm
Edition: 2nd ed. 1990. Softcover reprint of the origin

You may also be interested in...

Euclid's Elements
Added to basket
£21.99
Paperback
Proofs from THE BOOK
Added to basket
The Higher Arithmetic
Added to basket
The Theory of Algebraic Numbers
Added to basket
Wild Fibonacci
Added to basket
£5.99
Paperback
Numbers: A Very Short Introduction
Added to basket
Mathematics and Its History
Added to basket
Number Theory
Added to basket
£69.99
Paperback
Introduction to Complex Analysis
Added to basket
Elliptic Tales
Added to basket
£13.99
Paperback
Number Theory
Added to basket
£64.00
Hardback
An Introduction to the Theory of Numbers
Added to basket
Euclid's Elements
Added to basket
£31.99
Hardback
Elementary Number Theory
Added to basket
Love and Math
Added to basket
£18.99
Hardback

Reviews

Please sign in to write a review

Your review has been submitted successfully.