An Introduction to the Theory of Numbers

Produktbeschreibung

Much-needed update of a classic text Extensive end-of-chapter notes Suggestions for further reading for the more avid reader

New chapter on one of the most important developments in number theory and its role in the proof of Fermat's Last Theorem

New to this edition Revised end-of-chapter notes New chapter on elliptic curves

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. 

Inhaltsverzeichnis

* Preface to the sixth edition


* Preface to the fifth edition


* 1: The Series of Primes (1)


* 2: The Series of Primes (2)


* 3: Farey Series and a Theorem of Minkowski


* 4: Irrational Numbers


* 5: Congruences and Residues


* 6: Fermat's Theorem and its Consequences


* 7: General Properties of Congruences


* 8: Congruences to Composite Moduli


* 9: The Representation of Numbers by Decimals


* 10: Continued Fractions


* 11: Approximation of Irrationals by Rationals


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


* 13: Some Diophantine Equations


* 14: Quadratic Fields (1)


* 15: Quadratic Fields (2)


* 16: The Arithmetical Functions ø(n), ¿(n), *d(n), *s(n), r(n)


* 17: Generating Functions of Arithmetical Functions


* 18: The Order of Magnitude of Arithmetical Functions


* 19: Partitions


* 20: The Representation of a Number by Two or Four Squares


* 21: Representation by Cubes and Higher Powers


* 22: The Series of Primes (3)


* 23: Kronecker's Theorem


* 24: Geometry of Numbers


* 25: Joseph H. Silverman: Elliptic Curves


* Appendix


* List of Books


* Index of Special Symbols and Words


* Index of Names


* General Index 

Autoreninfo

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.