Algebraic number theory
著者
書誌事項
Algebraic number theory
（Graduate texts in mathematics, 110）
Springer-Verlag, c1994
2nd ed
- : us
- : gw
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注記
Includes bibliography (p. 353-354) and index
内容説明・目次
- 巻冊次
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: us ISBN 9780387942254
内容説明
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
目次
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.
- 巻冊次
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: gw ISBN 9783540942252
内容説明
This textbook covers all of the basic material of classical algebraic and analytic number theory, giving the student the background necessary for the study of modern algebraic number theory. Part I introduces some of the basic ideas of the theory: number fields, ideal classes, ideals and addles, and zeta functions. 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 which has been completely re-written for the new edition.
目次
Part I: General Basic Theory: 1. Algebraic Integers. 2. Completions. 3. The Different and Discriminant. 4. Cyclotomic Fields. 5. Paralellotopes. 6. The Ideal Function. 7. Ideles and Adeles. 8. Elementary Properties of the Zeta Function and L-series.- Part II: Class Field Theory: 9. Norm Index Computations. 10. The Artin Symbol, Reciprocity Law, and Class Field Theory. 11. The Existence Theorem and Local Class Field Theory. 12. L-series Again.- Part III: Analytic Theory: 13. Functional Equation of the Zeta Function, Hecke's Proof. 14. Functional Equation, Tate's Thesis. 15. Density of Primes and Tauberian Theorem. 16. The Brauer-Siegel Theorem. 17. Explicit Formulas.- Bibliography.- Index.
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