<quote>
Description
This volume is a translation of Dirichlet's <i>Vorlesungen \"uber
Zahlentheorie</i> which includes nine supplements by Dedekind and
an introduction by John Stillwell, who translated the volume.
<i>Lectures on Number Theory</i> 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
<i>Disquisitiones Arithmeticae</i> 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 mathematical works that served as cornerstones
for modern mathematical thought. (For another historical translation
by Professor Stillwell, see <i>Sources of Hyperbolic Geometry</i>,
volume 10 in the History of Mathematics series.)
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
Publisher: American Mathematical Society, London Mathematical Society
Distributor: American Mathematical Society
Series: History of Mathematics, ISSN: 0899-2428
Volume: 16
Publication Year: 1999
ISBN: 0-8218-2017-6
Paging: 275 pp.
Binding: Softcover
List Price: $49
</quote>
Reference: http://www.ams.org/bookstore/
Additional information: http://www.ams.org/bookstore/pspdf/hmath-16.pdf