This well-known 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.
Reihe
Auflage
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Editions-Typ
Illustrationen
Maße
Höhe: 216 mm
Breite: 138 mm
Gewicht
ISBN-13
978-3-540-94225-2 (9783540942252)
Schweitzer Klassifikation
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.
