Author | Ireland, Kenneth. author |
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Title | A Classical Introduction to Modern Number Theory [electronic resource] / by Kenneth Ireland, Michael Rosen |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1990 |
Edition | Second Edition |
Connect to | http://dx.doi.org/10.1007/978-1-4757-2103-4 |
Descript | XIV, 394 p. online resource |
1 Unique Factorization -- 2 Applications of Unique Factorization -- 3 Congruence -- 4 The Structure of U(?/n?) -- 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 -- Selected Hints for the Exercises