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Algebraic Number Theory

Front Cover
2 Reviews
Springer, Jun 24, 1994 - Mathematics - 357 pages
This is a 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. This new edition contains corrections, as well as several additions to the previous edition, and the last chapter on explicit formulas has been rewritten.
  

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User Review  - Joecolelife - Goodreads

Awesome text. For the more well-versed reader in Algebraic Number Theory. Great resource for a variety of topics. Read full review

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Contents

II
3
III
4
IV
8
V
11
VI
12
VII
18
VIII
22
IX
27
XLIX
200
L
206
LI
213
LII
215
LIII
217
LIV
219
LV
224
LVI
226

X
29
XI
31
XII
41
XIII
45
XIV
48
XV
51
XVI
57
XVII
62
XVIII
64
XIX
71
XX
76
XXI
82
XXII
96
XXIII
99
XXIV
110
XXV
116
XXVI
119
XXVII
123
XXVIII
128
XXIX
129
XXX
137
XXXI
139
XXXII
140
XXXIII
145
XXXIV
151
XXXV
152
XXXVI
155
XXXVII
159
XXXVIII
162
XXXIX
166
XL
170
XLI
173
XLII
179
XLIII
185
XLIV
187
XLV
190
XLVI
193
XLVII
195
XLVIII
197
LVII
229
LVIII
232
LIX
236
LX
241
LXI
245
LXII
250
LXIII
253
LXIV
260
LXV
262
LXVI
273
LXVII
275
LXVIII
276
LXIX
278
LXX
280
LXXI
282
LXXII
287
LXXIII
289
LXXIV
292
LXXV
297
LXXVI
303
LXXVII
304
LXXVIII
310
LXXIX
312
LXXX
315
LXXXI
321
LXXXII
322
LXXXIII
323
LXXXIV
325
LXXXV
327
LXXXVI
328
LXXXVII
331
LXXXVIII
333
LXXXIX
337
XC
344
XCI
348
XCII
353
XCIII
355
Copyright

Other editions - View all

Algebraic number theory
Algebraic number theory
Serge Lang
Snippet view - 1994
Algebraic number theory
Algebraic number theory
Serge Lang
Snippet view - 1986
Algebraic Number Theory
Algebraic Number Theory
Serge Lang
No preview available - 2013

Common terms and phrases

abelian extension adele algebraic integers archimedean absolute values Artin map assertion assume automorphism bounded Chapter character class field theory coefficients compact complex numbers concludes the proof conjugate contained converges Corollary cyclic cyclotomic decomposition group Dedekind ring define degree denote Dirichlet series discriminant embedded equal exists an element factor group finite extension finite number follows formula Fourier fractional ideal functional equation fundamental domain Galois extension Galois group given group G Hence homomorphism ideal class group idele induced inequality integral closure isomorphism kernel L-series lattice Lemma Let f Let K/k maximal ideal module multiplicative group non-zero notation number field number of elements obtain open subgroup p-adic positive integer prime ideal prime number Proposition prove quasi-character quotient field Re(s residue class field roots of unity satisfies splits completely subset surjective Theorem trivial unit unramified variables vector whence write zeta function

References to this book

From other books

Local Fields
Local Fields
Jean-Pierre Serre
No preview available - 1980
Introduction to Coding Theory
Introduction to Coding Theory
J H Van Lint
Limited preview - 1999
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From Google Scholar

Arithmetic Duality Theorems}
JS Milne - red
On Diagonal Algebraic Space–Time Block Codes
Mohamed Oussama Damen, Norman C Beaulieu - 2003 - IEEE TRANSACTIONS ON COMMUNICATIONS
The Iwasawa Invariant μp Vanishes for Abelian Number Fields
Bruce Ferrero, Lawrence C Washington - 1979 - Annals of Mathematics
Chern-Simons-Witten invariants of lens spaces and torus bundles ...
Lisa C Jeffrey - 1992 - Communications in Mathematical Physics
All Scholar search results »

References from web pages

11R: Algebraic number theory: global fields
There is also a mailing list "ALGEBRAIC-NUMBER-THEORY"; information is available at the Algebraic Number Theory Preprint Archive ...
www.math.niu.edu/ ~rusin/ known-math/ index/ 11RXX.html

Art of Problem Solving Forum
I have heard about Newkirch's Algebraic Number Theory as especially good. How is this compared to Lang's Algebraic Number Theory? ...
www.artofproblemsolving.com/ Forum/ viewtopic.php?p=717739

grants
Format: a semester-long seminar giving a rapid introduction to algebraic number theory and elliptic curves. Hopefully, the material will end up including ...
www.math.ucdavis.edu/ ~osserman/ seminar/

Review: Serge Lang, Algebraic Number Theory
Review: Serge Lang, Algebraic Number Theory. Lawrence Corwin. Source: Bull. Amer. Math. Soc. Volume 78, Number 5 (1972), 690-693. ...
projecteuclid.org/ handle/ euclid.bams/ 1183533968

Algebraic number field - Wikipedia, the free encyclopedia
Gerald J. Janusz, Algebraic Number Fields, second edition, American Mathematical Society, 1995; Serge Lang, Algebraic Number Theory, second edition, ...
en.wikipedia.org/ wiki/ Algebraic_number_field

Basic Library List-Number Theory
Algebraic Number Theory. Springer-Verlag New York, 1996. ISBN 0387942254 ... Pohst, Michael and Zassenshaus, H. Algorithmic Algebraic Number Theory. ...
www.maa.org/ BLL/ numtheory.htm

planetmath: bibliography for number theory
Serge Lang, Algebraic Number Theory. Springer-Verlag, New York. ... Cross-references: Galois cohomology, fields, algebraic number theory, multiplicative, ...
planetmath.org/ encyclopedia/ BibliographyForNumberTheory.html

Typeset by ams -tex 1
Henri Cohen, A course in computational algebraic number theory, Springer-Verlag, 1993. ... M.Pohst and H.Zassenhaus, Algorithmic algebraic number theory, ...
www.mth.uea.ac.uk/ ~h090/ bib.pdf

bibliografia
Ian Stewart, David Tall: Algebraic number theory. 2nd edition. Chapman y Hall, 1987. ... Henri Cohen: A course in computational algebraic number theory. ...
mate.dm.uba.ar/ ~krick/ BiblioTN.htm

CIRCULANTS (Extract)
[FT] "Algebraic Number Theory" by A. Frohlich & mj Taylor; Cambridge University ... [Lang] "Algebraic Number Theory" by Serge Lang; Springer-Verlag, 1986. ...
circulants.org/ circ/ Biblio.pdf

Bibliographic information

QR code for Algebraic Number Theory
TitleAlgebraic Number Theory
Volume 110 of Applied Mathematical Sciences
Volume 110 of Graduate Texts in Mathematics, ISSN 0072-5285
AuthorSerge Lang
Edition2, illustrated
PublisherSpringer, 1994
ISBN0387942254, 9780387942254
Length357 pages
Subjects › 

Mathematics / Number Theory
  
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