# Problems in Algebraic Number Theory

• M. Ram Murty
• Jody Esmonde
Book

Part of the Graduate Texts in Mathematics book series (GTM, volume 190)

1. Front Matter
Pages i-xvi
2. ### Problems

1. Pages 3-11
2. Pages 13-26
3. Pages 27-39
4. Pages 41-52
5. Pages 53-68
6. Pages 69-79
7. Pages 81-97
8. Pages 99-116
9. Pages 117-125
10. Pages 127-138
11. Pages 139-155
3. ### Solutions

1. Pages 159-178
2. Pages 179-196
3. Pages 197-206
4. Pages 207-225
5. Pages 227-244
6. Pages 245-262
7. Pages 263-278
8. Pages 279-298

### Introduction

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.

### Keywords

algebra algebraic number theory calculus linear algebra number theory

#### Authors and affiliations

• M. Ram Murty
• 1
• Jody Esmonde
• 2
1. 1.Department of Mathematics and StatisticsQueen's UniversityKingstonCanada
2. 2.Graduate School of EducationUniversity of California at BerkeleyBerkeleyUSA

### Bibliographic information

• DOI https://doi.org/10.1007/b138452