A classical introduction to modern number theory
Kenneth Ireland, Michael Rosen.
2nd ed.
New York : Springer-Verlag, ©1990.
xiv, 389 págs. ; 25 cm.
Serie: Graduate texts in mathematics ; 84
ISBN: 038797329X, 354097329X (Berlin)
"A revised and expanded version of Elements of number theory, published in 1972 by Bogden & Quigley."—Dorso port.
Incluye referencias bibliográficas (p. 375-384) e índice.
Reseña: MathSciNet, 92e:11001
Contenido
- 1. Unique factorization
- 2. Applications of unique factorization
- 3. Congruence
- 4. The structure of U(Z/nZ)
- 5. Quadratic reciprocity
- 6. Quadratic Gauss sums
- 7. Finite fields
- 8. Gauss and Jacobi sums
- 9. Cubic and biquadratic reciprocity
- 10. Equations over finite fields
- 11. The Zeta function
- 12. Algebraic number theory
- 13. Quadratic and cyclotomic fields
- 14. The Stickelberger relation and the Eisenstein reciprocity law
- 15. Bernoulli numbers
- 16. Dirichlet $L$-functions
- 17. Diophantine equations
- 18. Elliptic curves
- 19. The Mordell-Weil theorem
- 20. New progress in arithmetic geometry.
