Edition 
Second edition. 
Physical description 
1 online resource (xiv, 394 pages). 
Series 
Graduate Texts in Mathematics, 00725285 ; 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 LFunctions  Diophantine Equations  Elliptic Curves  The MordellWeil 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 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. 
Other author 
Rosen, Michael.

Subject 
Mathematics.


Number theory.


Electronic books. 
ISBN 
9781475721034 (electronic bk.) 

147572103X (electronic bk.) 

9781441930941 

1441930949 

147572103X 
