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. "Lang's books are always of great value for the graduate student and the research mathematician. This updated edition of Algebraic number theory is no exception."---MATHEMATICAL REVIEWS
Part I: General Basic Theory: Algebraic Integers. Completions. The Different and Discriminant. Cyclotomic Fields. Paralellotopes. The Ideal Function. Ideles and Adeles. Elementary Properties of the Zeta Function and L-series.- Part II: Class Field Theory: Norm Index Computations. The Artin Symbol, Reciprocity Law, and Class Field Theory. The Existence Theorem and Local Class Field Theory. L-series Again.- Part III: Analytic Theory: 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.- Bibliography.- Index.
Second Edition S. Lang Algebraic Number Theory "This book is the second edition of Lang's famous and indispensable book on algebraic number theory. The major change from the previous edition is that the last chapter on explicit formulas has been completely rewritten. In addition, a few new sections have been added to the other chapters ... Lang's books are always of great value for the graduate student and the research mathematician. This updated edition of Algebraic number theory is no exception."-MATHEMATICAL REVIEWS
ALGEBRAIC NUMBER THEORY 1994 C
1994. Corr. 3rd
Springer-Verlag New York Inc.
Country of Publication
Place of Publication
New York, NY
New Haven, CT, US
Applied Mathematical Sciences (Springer)