Algebraic Number Theory

From the review: “The present book has as its aim to resolve a discrepancy in the textbook literature and … to provide a comprehensive introduction to algebraic number theory which is largely based on the modern, unifying conception of (one-dimensional) arithmetic algebraic geometry. … Despite this exacting program, the book remains an introduction to algebraic number theory for the beginner… The author discusses the classical concepts from the viewpoint of Arakelov theory…. The treatment of class field theory is … particularly rich in illustrating complements, hints for further study, and concrete examples…. The concluding chapter VII on zeta-functions and L-series is another outstanding advantage of the present textbook…. The book is, without any doubt, the most up-to-date, systematic, and theoretically comprehensive textbook on algebraic number field theory available.”

W. Kleinert in: Zentralblatt für Mathematik, 1992

Table of Contents

Chapter I. Algebraic Integers

Chapter II. The Theory of Valuations

Chapter Ill. Riemann-Roch Theory

Chapter IV. Abstract Class Field Theory

Chapter V. Local Class Field Theory

Chapter VI. Global Class Field Theory

Chapter VII. Zeta Functions and L-series