Cyclotomic fields II. Front Cover. Serge Lang. Springer-Verlag, Cyclotomic Fields II · S. Lang Limited preview – QR code for Cyclotomic fields II. 57 CROWELL/Fox. Introduction to Knot. Theory. 58 KOBLITZ. p-adic Numbers, p- adic. Analysis, and Zeta-Functions. 2nd ed. 59 LANG. Cyclotomic Fields. In number theory, a cyclotomic field is a number field obtained by adjoining a complex primitive . New York: Springer-Verlag, doi/ , ISBN , MR · Serge Lang, Cyclotomic Fields I and II.

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The Formal Leopoldt Transform. The geometric problem for a general n can be reduced to the following question in Galois theory: I started studying algebraic number theory last summer by going through Marcus book. Sign up using Email and Password. Cyclotomic Fields I and II. Please help to improve this article by introducing more precise citations. Proof of Theorem 5 1. I am specifically interested in connection of cyclotomic fields and Bernoulli numbers.

Sign up using Facebook. Application of the Logarithm to the Local Symbol. So I would appreciate suggestions of books, or chapters in a book, lecture notes, etc.

The Maximal pabelian pramified Extension. I’m not familiar with Lang. Stickelberger Elements as Distributions.

The Index for k Even. Projective Limit of the Unit Groups. Gerry Myerson k 8 Measures and Power Series fieldd the Composite Case.

In particular, this led him to introduce, with Kubota, p-adic analogues of the complex L-functions attached to cyclotomic extensions of the rationals. Computation of Lp1 y in the Composite Case Contents. Gauss Sums over Extension Fields. Selected pages Title Page. If unique factorization of algebraic integers were true, then it could have been used to rule out the existence of nontrivial solutions to Fermat’s equation.


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].

The Index for k Odd. The Closure of the Cyclotomic Units. Kummer’s work on the congruences for the class numbers of cyclotomic fields was generalized in the twentieth century by Iwasawa in Iwasawa theory and by Kubota and Leopoldt in their theory of p-adic zeta functions. Maybe I need to read some cclotomic on algebraic number theory, I do not know. Jacobi Sums as Hecke Characters.

Cyclotomic fields II – Serge Lang – Google Books

Equidistribution and Normal Families. Finally, in the late ‘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. Ireland and Rosen, A Classical Introduction to Modern Number Theory, doesn’t get as far into algebraic number theory as the others, but it is well-written and has a chapter on cyclotomic fields and a chapter on Bernoulli numbers.

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. The Ideal Class Group of Qup.


Cyclotomic field

Iwasawa Invariants for Measures. The Index of the First Stickelberger Ideal. A Local Pairing with the Logarithmic Derivative.

If you read the first 4 chapters, you should have the necessary background for most of Washington’s book. Retrieved from ” https: The Main Theorem for the Symbol x xnn.


A cyclotomic field is the splitting field of the cyclotomic polynomial. Twistings and Stickelberger Ideals. The Mellin Transform and padic Lfunction.

This article includes a list of referencesbut its sources remain unclear because it has insufficient inline citations. September Learn how and when to remove this template message. End of the Proof of the Main Theorems. By using our site, you acknowledge that you have read and understand our Cookie AlngPrivacy Policyand our Terms of Service.

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 llang, and more generally, Galois extensions of number fields whose Galois group is isomorphic to the additive group of p-adic integers.

Application to the Bernoulli Distributions.