Problems in Algebraic Number Theory

M. Ram Murty, Jody Esmonde (auth.)0387221824, 9780387221823

From Reviews of the First Edition:

This book provides a problem-oriented first course in algebraic number theory. … The authors have done a fine job in collecting and arranging the problems. Working through them, with or without help from a teacher, will surely be a most efficient way of learning the theory. Many of the problems are fairly standard, but there are also problems of a more original type. This makes the book a useful supplementary text for anyone studying or teaching the subject. … This book deserves many readers and users.

– T. Metsänkylä , Mathematical Reviews

The book covers topics ranging from elementary number theory (such as the unique factorization of integers or Fermat’s little theorem) to Dirichlet’s theorem about primes in arithmetic progressions and his class number formula for quadratic fields, and it treats standard material such as Dedekind domains, integral bases, the decomposition of primes not dividing the index, the class group, the Minkowski bound and Dirichlet’s unit theorem … the reviewer is certain that many students will benefit from this pathway into the fascinating realm of algebraic number theory.

– Franz Lemmermeyer, Zentralblatt

This second edition is an expanded and revised version of the first edition. In particular, it contains an extra chapter on density theorems and $L$-functions highlighting some of the analytic aspects of algebraic number theory.

Table of contents :
Elementary Number Theory….Pages 3-11
Euclidean Rings….Pages 13-26
Algebraic Numbers and Integers….Pages 27-39
Integral Bases….Pages 41-52
Dedekind Domains….Pages 53-68
The Ideal Class Group….Pages 69-79
Quadratic Reciprocity….Pages 81-97
The Structure of Units….Pages 99-116
Higher Reciprocity Laws….Pages 117-125
Analytic Methods….Pages 127-138
Density Theorems….Pages 139-155
Elementary Number Theory….Pages 159-178
Euclidean Rings….Pages 179-196
Algebraic Numbers and Integers….Pages 197-206
Integral Bases….Pages 207-225
Dedekind Domains….Pages 227-244
The Ideal Class Group….Pages 245-262
Quadratic Reciprocity….Pages 263-278
The Structure of Units….Pages 279-298
Higher Reciprocity Laws….Pages 299-311
Analytic Methods….Pages 313-331
Density Theorems….Pages 333-346