Lectures on Number Theory: (History of Mathematics)

This volume is a translation of Dirichlet's Vorlesungen uber 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. This book is the first in an informal sequence of works to be included within the History of Mathematics series, co-published by the AMS and the London Mathematical Society. Volumes to be published within this subset are classical

Table of Contents:
On the divisibility of numbers On the congruence of numbers On quadratic residues On quadratic forms Determination of the class number of binary quadratic forms Some theorems from Gauss's theory of circle division On the limiting value of an infinite series A geometric theorem Genera of quadratic forms Power residues for composite moduli Primes in arithmetic progressions Some theorems from the theory of circle division On the Pell equation Convergence and continuity of some infinite series Index.