Number Theory 2: Algebraic Number Theory
β A. N. Parshin, I. R. Shafarevich
π Library
π
1992
π Springer
π English
β¦ LIBER β¦
π
Algebraic Number Theory
β Scribed by JΓΌrgen Neukirch (auth.)
- Publisher
- Springer-Verlag Berlin Heidelberg
- Year
- 1999
- Tongue
- English
- Leaves
- 590
- Series
- Grundlehren der mathematischen Wissenschaften 322
- Edition
- 1
- Category
- Library
β¬ Acquire This Volume
No coin nor oath required. For personal study only.
β¦ Synopsis
"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is liable to become a classic; the more so as recent developments have been taken into account which will not be outdated quickly.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
β¦ Table of Contents
Front Matter....Pages i-xvii
Algebraic Integers....Pages 1-97
The Theory of Valuations....Pages 99-181
Riemann-Roch Theory....Pages 183-260
Abstract Class Field Theory....Pages 261-315
Local Class Field Theory....Pages 317-355
Global Class Field Theory....Pages 357-417
Zeta Functions and L -series....Pages 419-549
Back Matter....Pages 551-574
β¦ Subjects
Number Theory
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