Algebraic number theory

Serge Lang

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

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  • One General Basic Theory.- I Algebraic Integers.- II Completions.- III The Different and Discriminant.- IV Cyclotomic Fields.- V Parallelotopes.- VI The Ideal Function.- VII Ideles and Adeles.- VIII Elementary Properties of the Zeta Function and L-series.- Two Class Field Theory.- IX Norm Index Computations.- X The Artin Symbol, Reciprocity Law, and Class Field Theory.- XI The Existence Theorem and Local Class Field Theory.- XII L-series Again.- Three Analytic Theory.- XIII Functional Equation of the Zeta Function, Hecke's Proof.- XIV Functional Equation, Tate's Thesis.- XV Density of Primes and Tauberian Theorem.- XVI The Brauer-Siegel Theorem.- XVII Explicit Formulas.

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書名 Algebraic number theory
著作者等 Lang, Serge
シリーズ名 Graduate texts in mathematics
出版元 Springer-Verlag
刊行年月 c1994
版表示 2nd ed
ページ数 xiii, 357 p.
大きさ 24 cm
ISBN 3540942254
NCID BA23060424
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言語 英語
出版国 アメリカ合衆国