The Prime Number Theorem
The Prime Number Theorem
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 (in an approximate but well-defined sense) how many primes can be found that are less than any integer. The prime number theorem tells what this formula is and it is indisputably one of the the great classical theorems of mathematics. This textbook introduces the prime number theorem and is suitable for advanced undergraduates and beginning graduate students. The author deftly shows how analytical tools can be used in number theory to attack a 'real' problem.
- Fascinating classical subject
- Class-tested by the author
- Provides an alternative view of the topic
Reviews & endorsements
"...strongly recommended to those wishing to teach some analytic number theory at the undergraduate level." Mathematical Reviews
Product details
April 2003Paperback
9780521891103
264 pages
228 × 160 × 14 mm
0.39kg
1 b/w illus.
Available
Table of Contents
- 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.
