Lectures on Number Theory

Includes index

Includes bibliography references

Ch. 1. On the divisibility of numbers Ch. 2. On the congruence of numbers Ch. 3. On quadratic residues Ch. 4. On quadratic forms Ch. 5. Determination of the class number of binary quadratic forms Supplement I. Some theorems from Gauss's theory of circle division Supplement II. On the limiting value of an infinite series Supplement III. A geometric theorem Supplement IV. Genera of quadratic forms Supplement V. Power residues for composite moduli Supplement VI. Primes in arithmetic progressions Supplement VII. Some theorems from the theory of circle division Supplement VIII. On the Pell equation Supplement IX. Convergence and continuity of some infinite series.

This volume is a translation of Dirichlet's Vorlesungen über Zahlentheorie which includes nine supplements by Dedekind and an introduction by John Stillwell, who translated the volume. Lectures on Number Theory is the first of its kind on the subject matter. It covers most of the topics that are standard in a modern first course on number theory, but also includes Dirichlet's famous results on class numbers and primes in arithmetic progressions. The book is suitable as a textbook, yet it also offers a fascinating historical perspective that links Gauss with modern number theory. The legendary story is told how Dirichlet kept a copy of Gauss's Disquisitiones Arithmeticae with him at all times and how Dirichlet strove to clarify and simplify Gauss's results. Dedekind's footnotes document what material Dirichlet took from Gauss, allowing insight into how Dirichlet transformed the ideas into essentially modern form. Also shown is how Gauss built on a long tradition in number theory-going back to Diophantus-and how it set the agenda for Dirichlet's work. This important book combines historical perspective with transcendent mathematical insight. The material is still fresh and presented in a very readable fashion.