An Introduction to the Theory of Numbers

by Hardy, G. H.; Wright, Edward M.; Heath-Brown, Roger; Silverman, Joseph; Wiles, Andrew

• ISBN13: 9780199219865
• ISBN10: 0199219869
• Edition: 6th
• Format: Paperback
• Copyright: 2008-09-15
• Publisher: Oxford University Press

Summary

An Introduction to the Theory of Numbers by G. H. Hardy and E. M. Wright is found on the reading list of virtually all elementary number theory courses and is widely regarded as the primary and classic text in elementary number theory. Developed under the guidance of D. R. Heath-Brown, this Sixth Edition of An Introduction to the Theory of Numbers has been extensively revised and updated to guide today's students through the key milestones and developments in number theory. Updates include a chapter by J. H. Silverman on one of the most important developments in number theory -- modular elliptic curves and their role in the proof of Fermat's Last Theorem -- a foreword by A. Wiles, and comprehensively updated end-of-chapter notes detailing the key developments in number theory. Suggestions for further reading are also included for the more avid reader. The text retains the style and clarity of previous editions making it highly suitable for undergraduates in mathematics from the first year upwards as well as an essential reference for all number theorists.

Author Biography

Roger Heath-Brown F.R.S. was born in 1952, and is currently Professor of
Pure Mathematics at Oxford University. He works in analytic number
theory, and in particular on its applications to prime numbers and to
Diophantine equations.

Table of Contents

Preface to the sixth edition Andrew Wiles Preface to the fifth edition

The Series of Primes (1)

The Series of Primes (2)

Farey Series and a Theorem of Minkowski

Irrational Numbers

Congruences and Residues

Fermat's Theorem and its Consequences

General Properties of Congruences

Congruences to Composite Moduli

The Representation of Numbers by Decimals

Continued Fractions

Approximation of Irrationals by Rationals

The Fundamental Theorem of Arithmetic in k(l), k(i), and k(p)

Some Diophantine Equations

Quadratic Fields (1)

Quadratic Fields (2)

The Arithmetical Functions ø(n), m(n), d(n), ¿(n), r(n)

Generating Functions of Arithmetical Functions

The Order of Magnitude of Arithmetical Functions

Partitions

The Representation of a Number by Two or Four Squares

Representation by Cubes and Higher Powers

The Series of Primes (3)

Kronecker's Theorem

Geometry of Numbers

Elliptic Curves, Joseph H. Silverman

Appendix

List of Books

Index of Special

Symbols and Words

Index of Names General

Index

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