# Lectures on Number Theory

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*P. G. L. Dirichlet; R. Dedekind*

A co-publication of the AMS and the London Mathematical Society

This volume is a translation of Dirichlet's

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

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 volume is one of an informal sequence of works within the
History of Mathematics series. Volumes in this subset,
“Sources”, are classical mathematical works that served as
cornerstones for modern mathematical thought. (For
another historical translation by Professor Stillwell, see

#### Reviews & Endorsements

A new edition of Dirichlet's *Lectures on Number Theory* would be big
news any day, but it's particularly gratifying to see the book appear as
“the first of an informal sequence” which is to include “classical
mathematical works that served as cornerstones for modern mathematical
thought.” So all power to the American Mathematical Society and the London
Mathematical Society in their joint-venture History of Mathematics
series: may the “Sources” subseries live long and prosper. [T]his is quite
accessible, and could almost be used as a textbook still today. For those
who like to heed Abel's admonition to “read the masters, not their
students,” here's a great opportunity to learn more about Number Theory.

-- MAA Online

This is a nice English edition of Dirichlet's famous

-- European Mathematical Society Newsletter

#### Table of Contents

# Table of Contents

## Lectures on Number Theory

- Cover Cover11
- Title page v6
- Contents vii8
- Translator’s introduction xi12
- On the divisibility of numbers 122
- On the congruence of numbers 2142
- On quadratic residues 5374
- On quadratic forms 91112
- Determination of the class number of binary quadratic forms 149170
- Supplement I. Some theorems from Gauss’s theory of circle division 199220
- Supplement II. On the limiting value of an infinite series 211232
- Supplement III. A geometric theorem 215236
- Supplement IV. Genera of quadratic forms 217238
- Supplement V. Power residues for composite moduli 229250
- Supplement VI. Primes in arithmetic progressions 237258
- Supplement VII. Some theorems from the theory of circle division 249270
- Supplement VIII. On the Pell equation 257278
- Supplement IX. Convergence and continuity of some infinite series 261282
- Index 269290
- Back Cover Back Cover1297