A classical introduction to modern number theory
The second edition of this book which bridges the gap between elementary number theory and the systematic study of advanced topics. New topics include a proof of Mordell's fundamental theorem, and an overview of Flating's proof of the Mordell conjecture.
Einführung
xiv, 389 p. ; 24 cm.
9780387973296, 9783540973294, 9780387906256, 038797329X, 354097329X, 0387906258
318356339
Contents: Unique Factorization.- Applications of Unique Factorization.- Congruence.- The Structure of U(Z/nZ).- Quadratic Reciprocity.- Quadratic Gauss Sums.- Finite Fields.- Gauss and Jacobi Sums.- Cubic and Biquadratic Reciprocity.- Equations Over Finite Fields.- The Zeta Function.- Algebraic Number Theory.- Quadratic and Cyclotomic Fields.- The Stickelberger Relation and the Eisenstein Reciprocity Law.- Bernoulli Numbers.- Dirichlet L-Functions.- Diophantine Equations.- Elliptic Curves.- The Mordell-Weil Theorem.- New Progress in Arithmetic Geometry.- Selected Hints for the Exercises.