An Introduction to the Theory of Numbers

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OUP Oxford, Jul 31, 2008 - Mathematics - 621 pages
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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.
 

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Contents

I THE SERIES OF PRIMES 1
1
II THE SERIES OF PRIMES 2
14
III FAREY SERIES AND A THEOREM OF MINKOWSKI
28
IV IRRATIONAL NUMBERS
45
V CONGRUENCES AND RESIDUES
57
VI FERMATS THEOREM AND ITS CONSEQUENCES
78
VII GENERAL PROPERTIES OF CONGRUENCES
103
VIII CONGRUENCES TO COMPOSITE MODULI
120
XVII GENERATING FUNCTIONS OF ARITHMETICAL FUNCTIONS
318
XVIII THE ORDER OF MAGNITUDE OF ARITHMETICAL FUNCTIONS
342
XIX PARTITIONS
361
XX THE REPRESENTATION OF A NUMBER BY TWO OR FOUR SQUARES
393
XXI REPRESENTATION BY CUBES AND HIGHER POWERS
419
XXII THE SERIES OF PRIMES 3
451
XXIII KRONECKERS THEOREM
501
XXIV GEOMETRY OF NUMBERS
523

IX THE REPRESENTATION OF NUMBERS BY DECIMALS
138
X CONTINUED FRACTIONS
165
XI APPROXIMATION OF IRRATIONALS BY RATIONALS
198
XII THE FUNDAMENTAL THEOREM OF ARITHMETIC IN k1 ki AND k961
229
XIII SOME DIOPHANTINE EQUATIONS
245
XIV QUADRATIC FIELDS 1
264
XV QUADRATIC FIELDS 2
283
XVI THE ARITHMETICAL FUNCTIONS 216n 956n dn 963n rn
302
XXV ELLIPTIC CURVES
549
Appendix
593
A List of Books
597
Index of Special Symbols and Words
601
Index of Names
605
General Index
611
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About the author (2008)


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.

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