The Prime Number Theorem

This textbook demonstrates how the tools of analysis can be used in number theory to attack a famous problem.

G. J. O. Jameson (Author)

9780521891103, Cambridge University Press

Paperback, published 17 April 2003

264 pages, 1 b/w illus.
22.8 x 16 x 1.4 cm, 0.39 kg

'The book is engagingly written, in a friendly style, and there are short biographies of the mathematicians most associated with the prime number theorem. Given the complexity and depth of the mathematics needed, I doubt that a more accessible account of the theorem exists.' The Mathematical Gazette

At first glance the prime numbers appear to be distributed in a very irregular way amongst the integers, but it is possible to produce a simple formula that tells us (in an approximate but well defined sense) how many primes we can expect to find that are less than any integer we might choose. The prime number theorem tells us what this formula is and it is indisputably one of the great classical theorems of mathematics. This textbook gives an introduction to the prime number theorem suitable for advanced undergraduates and beginning graduate students. The author's aim is to show the reader how the tools of analysis can be used in number theory to attack a 'real' problem, and it is based on his own experiences of teaching this material.

Preface
1. Foundations
2. Some important Dirichlet series and arithmetic functions
3. The basic theorems
4. Prime numbers in residue classes: Dirichlet's theorem
5. Error estimates and the Riemann hypothesis
6. An 'elementary' proof of the prime number theorem
Appendices
Bibliography
Index.

Subject Areas: Number theory [PBH]