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Princeton University Library Catalog
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Algebraic number theory / Serge Lang.
Author
Lang, Serge, 1927-2005
[Browse]
Format
Book
Language
English
Εdition
2nd ed.
Published/Created
New York : Springer-Verlag, ©1994.
Description
xiii, 357 p. : ill. ; 24 cm.
Availability
Copies in the Library
Location
Call Number
Status
Location Service
Notes
Lewis Library - Stacks
QA247 .L29 1994
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Lewis Library - Stacks
QA247 .L29 1994
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Details
Subject(s)
Algebraic number theory
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Series
Graduate texts in mathematics ; 110.
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Summary note
Publisher Description (unedited publisher data) This is a corrected printing of the second edition of Lang's well-known textbook. It covers all of the basic material of classical algebraic number theory, giving the student the background necessary for the study of further topics in algebraic number theory, such as cyclotomic fields, or modular forms. Part I introduces some of the basic ideas of the theory: number fields, ideal classes, ideles and adeles, and zeta functions. It also contains a version of a Riemann-Roch theorem in number fields, proved by Lang in the very first version of the book in the sixties. This version can now be seen as a precursor of Arakelov theory. Part II covers class field theory, and Part III is devoted to analytic methods, including an exposition of Tate's thesis, the Brauer-Siegel theorem, and Weil's explicit formulas. The second edition contains corrections, as well as several additions to the previous edition, and the last chapter on explicit formulas has been rewritten.
Bibliographic references
Includes bibliographical references (p. 353-354) and index.
Contents
Algebraic integers
Completions
The different and discriminant
Cyclotomic fields
Parallelotopes
The ideal function
Ideles and adeles
Elementary properties of the zeta function and L-series
Norm index computations
The Artin symbol, reciprocity law, and class field theory
The existence theorem and local class field theory
L-series again
Functional equation of the zeta function, Hecke's proof
Functional equation, Tate's thesis
Density of primes and Tauberian theorem
The Brauer-Siegel theorem
Explicit formulas.
Show 14 more Contents items
ISBN
0387942254 ((New York))
9780387942254 ((New York))
3540942254 ((Berlin))
9783540942252 ((Berlin))
LCCN
93050625
OCLC
29667945
International Article Number
9780387942254
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