An Introduction to Sieve Methods and Their Applications

This book provides a motivated introduction to sieve theory.

Alina Carmen Cojocaru (Author), M. Ram Murty (Author)

9780521612753, Cambridge University Press

Paperback, published 8 December 2005

238 pages, 275 exercises
22.9 x 16.1 x 1.2 cm, 0.34 kg

'… the shortest and simplest book on sieve methods that I have seen … beginners will appreciate the clear path laid out towards the modern theory. I enthusiastically recommend [this] book to any newcomer to the subject.' Frank Thorne, Bulletin of the American Mathematical Society

Sieve theory has a rich and romantic history. The ancient question of whether there exist infinitely many twin primes (primes p such that p+2 is also prime), and Goldbach's conjecture that every even number can be written as the sum of two prime numbers, have been two of the problems that have inspired the development of the theory. This book provides a motivated introduction to sieve theory. Rather than focus on technical details which can obscure the beauty of the theory, the authors focus on examples and applications, developing the theory in parallel. The text can be used for a senior level undergraduate course or an introductory graduate course in analytic number theory, and non-experts can gain a quick introduction to the techniques of the subject.

1. Some basic notions
2. Some elementary sieves
3. The normal order method
4. The Turan sieve
5. The sieve of Eratosthenes
6. Brun's sieve
7. Selberg's sieve
8. The large sieve
9. The Bombieri-Vinogradov theorem
10. The lower bound sieve
11. New directions in sieve theory
Bibliography.

Subject Areas: Number theory [PBH]