Description 
1 online resource (viii, 190 pages) : illustrations 
Series 
Contemporary mathematics, 02714132 ; 15 

Contemporary mathematics (American Mathematical Society) ; 15.

Contents 
Introduction  Galois theory of infinite extensions  Projective limits  Elementary theory of ℓadic 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 quasicharacters of idele class groups, SatoTate 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 185188), 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 
