A Classical Introduction to Modern Number Theory / Edition 2

A Classical Introduction to Modern Number Theory / Edition 2

by Kenneth Ireland, Michael Rosen
     
 

This well-developed, accessible text details the historical development of the subject throughout. It also provides wide-ranging coverage of significant results with comparatively elementary proofs, some of them new. This second edition contains two new chapters that provide a complete proof of the Mordel-Weil theorem for elliptic curves over the rational numbers

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Overview

This well-developed, accessible text details the historical development of the subject throughout. It also provides wide-ranging coverage of significant results with comparatively elementary proofs, some of them new. This second edition contains two new chapters that provide a complete proof of the Mordel-Weil theorem for elliptic curves over the rational numbers and an overview of recent progress on the arithmetic of elliptic curves.

Product Details

ISBN-13:
9780387973296
Publisher:
Springer New York
Publication date:
09/07/1990
Series:
Graduate Texts in Mathematics Series, #84
Edition description:
2nd ed. 1990. Corr. 5th printing 1998
Pages:
394
Product dimensions:
1.00(w) x 6.14(h) x 9.21(d)

Related Subjects

Table of Contents

1: Unique Factorization. 2: Applications of Unique Factorization. 3: Congruence. 4: The Structure of U. 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.

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