Author | Ireland, Kenneth. author |
---|---|

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 |

SUMMARY

Bridging the gap between elementary number theory and the systematic study of advanced topics, A Classical Introduction to Modern Number Theory is a well-developed and accessible text that requires only a familiarity with basic abstract algebra. Historical development is stressed throughout, along with wide-ranging coverage of significant results with comparatively elementary proofs, some of them new. An extensive bibliography and many challenging exercises are also included. This second edition has been corrected and contains two new chapters which provide a complete proof of the Mordell-Weil theorem for elliptic curves over the rational numbers, and an overview of recent progress on the arithmetic of elliptic curves

CONTENT

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

Mathematics
Number theory
Mathematics
Number Theory