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E-book
Author Ireland, Kenneth., author

Title A Classical Introduction to Modern Number Theory / by Kenneth Ireland, Michael Rosen
Edition Second edition
Published New York, NY : Springer New York : Imprint : Springer, 1990
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Description 1 online resource (XIV, 394 pages) : online resource
Series Graduate Texts in Mathematics, 0072-5285 ; 84
Graduate texts in mathematics ; 84. 0072-5285
Contents 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
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
Notes Bibliographic Level Mode of Issuance: Monograph
English
Subject Mathematics.
Number theory.
Mathematics.
Number theory.
Form Electronic book
Author Rosen, Michael., author
ISBN 147572103X
9781475721034