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Algebraic Number Theory

Author: Jürgen Neukirch
Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 1999.
Series: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 322.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
"The present book has as its aim to resolve a discrepancy in the textbook literature and ... to provide a comprehensive introduction to algebraic number theory which is largely based on the modern, unifying conception of (one-dimensional) arithmetic algebraic geometry. ... Despite this exacting program, the book remains an introduction to algebraic number theory for the beginner ... The author discusses the  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Jürgen Neukirch
ISBN: 9783662039830 3662039834
OCLC Number: 851391469
Description: 1 online resource (xvii, 574 pages).
Contents: Algebraic Integers --
The Theory of Valuations --
Riemann-Roch Theory --
Abstract Class Field Theory --
Local Class Field Theory --
Global Class Field Theory --
Zeta Functions and L-series --
Bibliography --
Index.
Series Title: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 322.
Responsibility: by Jürgen Neukirch.

Abstract:

This introduction to algebraic number theory discusses the classical concepts from the viewpoint of Arakelov theory. The treatment of class theory is particularly rich in illustrating complements,  Read more...

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hful and unabridged reprint of the original edition of J. Neukirch's excellent textbook on modern algebraic number theory ... . this unique classic in algebraic number theory is certainly of the Read more...

 
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   schema:description ""The present book has as its aim to resolve a discrepancy in the textbook literature and ... to provide a comprehensive introduction to algebraic number theory which is largely based on the modern, unifying conception of (one-dimensional) arithmetic algebraic geometry. ... Despite this exacting program, the book remains an introduction to algebraic number theory for the beginner ... The author discusses the classical concepts from the viewpoint of Arakelov theory ... The treatment of class field theory is ... particularly rich in illustrating complements, hints for further study, and concrete examples ... The concluding chapter VII on zeta-functions and L-series is another outstanding advantage of the present textbook ... The book is, without any doubt, the most up-to-date, systematic, and theoretically comprehensive textbook on algebraic number field theory available." W. Kleinert in Z.blatt f. Math., 1992 "The author's enthusiasm for this topic is rarely as evident for the reader as in this book. - A good book, a beautiful book." F. Lorenz in Jber. DMV 1995 "The present work is written in a very careful and masterly fashion. It does not show the pains that it must have caused even an expert like Neukirch. It undoubtedly is liable to become a classic; the more so as recent developments have been taken into account which will not be outdated quickly. Not only must it be missing from the library of no number theorist, but it can simply be recommended to every mathematician who wants to get an idea of modern arithmetic." J. Schoissengeier in Montatshefte Mathematik 1994."@en ;
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