Description 
1 online resource (XIV, 394 pages) : online resource 
Series 
Graduate Texts in Mathematics, 00725285 ; 84 

Graduate texts in mathematics ; 84. 00725285

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 Lfunctions  17 Diophantine Equations  18 Elliptic Curves  19 The MordellWeil 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 welldeveloped and accessible text that requires only a familiarity with basic abstract algebra. Historical development is stressed throughout, along with wideranging 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 MordellWeil 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 
