| Description |
1 online resource (viii, 190 pages) : illustrations |
| Series |
Contemporary mathematics, 0271-4132 ; 15 |
|
Contemporary mathematics (American Mathematical Society) ; 15.
|
| Contents |
Introduction -- Galois theory of infinite extensions -- Projective limits -- Elementary theory of ℓ-adic integration -- Ramification theory -- Multiplicative versus additive reduction -- Ramification of Abelian extensions -- The Weil groups of a local field -- Shafarevitch's theorem -- The Herbrand distribution |
| Summary |
These notes are intended as an introduction to those aspects of analytic number theory which depend on and have applications to the algebraic numbers. As is well known the central problem of the theory general algebraic formulation of ·the following distribution results: number theorem, Dirichlet's theorem on primes in arithmetic progressions, Cebotarev's density theorem on the distribution of Frobenius conjugacy classes in Galois groups, Hecke's density theorem on the distribution of the arguments of quasi-characters of idele class groups, Sato-Tate conjectural densities for the value distribution of the traces of Frobenius elements, strong multiplicity one theorem for automorphic representations of the general linear group, etc. These are all variants of a specific fundamental distribution problem. The principle aim of these notes is to develop these formulas and to give some of their applications |
| Bibliography |
Includes bibliographical references (pages 185-188), and index |
| Notes |
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL |
|
Online resource; title from PDF title page (ebrary, viewed May 23, 2014) |
|
digitized 2010 HathiTrust Digital Library committed to preserve pda MiAaHDL |
| Subject |
Number theory.
|
|
Algebraic fields.
|
|
Algebraic fields
|
|
Number theory
|
|
Analytische Zahlentheorie
|
|
Algebraischer Körper
|
|
Zahlentheorie
|
|
Teoria Dos Numeros.
|
|
Teoria Analitica Dos Numeros.
|
|
Nombres, Théorie des.
|
|
Corps algébriques.
|
| Genre/Form |
Instructional and educational works
|
|
Instructional and educational works.
|
|
Matériel d'éducation et de formation.
|
| Form |
Electronic book
|
| ISBN |
9780821876015 |
|
0821876015 |
|
