Table of Contents

Problems.- Elementary Number Theory.- Euclidean Rings.- Algebraic Numbers and Integers.- Integral Bases.- Dedekind Domains.- The Ideal Class Group.- Quadratic Reciprocity.- The Structure of Units.- Higher Reciprocity Laws.- Analytic Methods.- Density Theorems.- Solutions.- Elementary Number Theory.- Euclidean Rings.- Algebraic Numbers and Integers.- Integral Bases.- Dedekind Domains.- The Ideal Class Group.- Quadratic Reciprocity.- The Structure of Units.- Higher Reciprocity Laws.- Analytic Methods.- Density Theorems.

Promotional Information

2nd edition

Reviews

From the reviews of the second edition: "Problems in Algebraic Number Theory is intended to be used by the students for independent study of the subject. It provides the reader with a large collection of problems (about 500) ... . The reviewer thinks that the authors have done a fantastic job choosing the problems, which are perfectly arranged so the students can progressively move from topic to topic ... . the book is an excellent resource for the instructor and the student as a companion to any algebraic number theory course." (Alvaro Lozano-Robledo, MathDL, May, 2005) "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. ... the reviewer is certain that many students will benefit from this pathway into the fascinating realm of algebraic number theory." (Zentralblatt fur Didaktik der Mathematik, August, 2005) "This is the second edition of Problems in algebraic number theory. ... errors have been corrected ... . The decision to expand the book by including a chapter on density theorems is most welcome." (Franz Lemmermeyer, Zentralblatt MATH, Vol. 1055) "This is the second edition of an unusual introduction to algebraic number theory. ... each chapter is written in straightforward textbook style. All chapters contain a very large number of problems. ... it presents a good way of acquiring a working knowledge of basic algebraic number theory by using it for independent study or as supplementary reading." (Ch. Baxa, Monatshefte fur Mathematik, Vol. 149 (4), 2006)