An introduction to sieve methods and their applications
著者
書誌事項
An introduction to sieve methods and their applications
（London Mathematical Society student texts, 66）
Cambridge University Press, 2006, c2005
- : hardback
- : pbk
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注記
Bibliography: p. 218-221
Includes index
内容説明・目次
内容説明
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.
目次
- 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.
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