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Algebraic Number Theory : Grundlehren Der Mathematischen Wissenschaften (Springer Hardcover) - Jurgen Neukirch

Algebraic Number Theory

Grundlehren Der Mathematischen Wissenschaften (Springer Hardcover)

Hardcover Published: June 1999
ISBN: 9783540653998
Number Of Pages: 571

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From the review: "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: Zentralblatt für Mathematik, 1992

Industry Reviews

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 highest advantage for new generations of students, teachers, and researchers in German-speaking mathematical communities, and therefore more than welcome. ... it will remain as one of the valuables in the legacy of an outstanding researcher and teacher in algebraic number theory forever." (Werner Kleinert, Zentralblatt MATH, Vol. 1131 (9), 2008)

Algebraic Integersp. 1
The Gaussian Integersp. 1
Integralityp. 5
Idealsp. 16
Latticesp. 23
Minkowski Theoryp. 28
The Class Numberp. 34
Dirichlet's Unit Theoremp. 39
Extensions of Dedekind Domainsp. 44
Hilbert's Ramification Theoryp. 53
Cyclotomic Fieldsp. 58
Localizationp. 65
Ordersp. 72
One-dimensional Schemesp. 84
Function Fieldsp. 94
The Theory of Valuationsp. 99
The p-adic Numbersp. 99
The p-adic Absolute Valuep. 106
Valuationsp. 116
Completionsp. 123
Local Fieldsp. 134
Henselian Fieldsp. 143
Unramified and Tamely Ramified Extensionsp. 152
Extensions of Valuationsp. 160
Galois Theory of Valuationsp. 166
Higher Ramification Groupsp. 176
Riemann-Roch Theoryp. 183
Primesp. 183
Different and Discriminantp. 194
Riemann-Rochp. 208
Metrized O-Modules xvip. 224
Grothendieck Groupsp. 233
The Chern Characterp. 243
Grothendieck-Riemann-Rochp. 246
The Euler-Minkowski Characteristicp. 255
Abstract Class Field Theoryp. 261
Infinite Galois Theoryp. 261
Projective and Inductive Limitsp. 265
Abstract Galois Theoryp. 275
Abstract Valuation Theoryp. 284
The Reciprocity Mapp. 290
The General Reciprocity Lawp. 299
The Herbrand Quotientp. 310
Local Class Field Theoryp. 317
The Local Reciprocity Lawp. 317
The Norm Residue Symbol over Qpp. 327
The Hilbert Symbolp. 333
Formal Groupsp. 341
Generalized Cyclotomic Theoryp. 346
Higher Ramification Groupsp. 352
Global Class Field Theoryp. 357
Ideles and Idele Classesp. 357
Ideles in Field Extensionsp. 368
The Herbrand Quotient of the Idele Class Groupp. 373
The Class Field Axiomp. 380
The Global Reciprocity Lawp. 385
Global Class Fieldsp. 395
The Ideal-Theoretic Version of Class Field Theoryp. 405
The Reciprocity Law of the Power Residuesp. 414
Zeta Functions and L-seriesp. 419
The Riemann Zeta Functionp. 419
Dirichlet L-seriesp. 434
Theta Seriesp. 443
The Higher-dimensional Gamma Functionp. 453
The Dedekind Zeta Functionp. 457
Hecke Charactersp. 470
Theta Series of Algebraic Number Fieldsp. 484
Hecke L-seriesp. 493
Values of Dirichlet L-series at Integer Pointsp. 504
Artin L-seriesp. 517
The Artin Conductorp. 527
The Functional Equation of Artin L-seriesp. 535
Density Theoremsp. 542
Bibliographyp. 551
Indexp. 559
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540653998
ISBN-10: 3540653996
Series: Grundlehren Der Mathematischen Wissenschaften (Springer Hardcover)
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 571
Published: June 1999
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.37 x 16.0  x 3.81
Weight (kg): 0.93

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