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Author Ireland, Kenneth.

Title A Classical Introduction to Modern Number Theory [electronic resource] / by Kenneth Ireland, Michael Rosen.

Published New York, NY : Springer New York, 1990.


Location Call No. Status
Edition Second edition.
Physical description 1 online resource (xiv, 394 pages).
Series Graduate Texts in Mathematics, 0072-5285 ; 84
Graduate texts in mathematics ; 84.
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 -- Bibliography -- Index.
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.
Other author Rosen, Michael.
Subject Mathematics.
Number theory.
Electronic books.
ISBN 9781475721034 (electronic bk.)
147572103X (electronic bk.)