An Introduction to the Theory of Numbers

Informationen zum Autor
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.



...remains invaluable as a first course on the subject, and as a source of food for thought for anyone wishing to strike out on his own.

Autorentext
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.

Klappentext
The sixth edition of the classic undergraduate text in elementary number theory includes a new chapter on elliptic curves and their role in the proof of Fermat's Last Theorem, a foreword by Andrew Wiles and extensively revised and updated end-of-chapter notes.

Inhalt
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

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