An Introduction to Sieve Methods and Their Applications

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Cambridge University Press, Dec 8, 2005 - Mathematics - 224 pages
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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 motivating 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.
 

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Contents

Some elementary sieves
15
The normal order method
32
The Turan sieve
47
The sieve of Eratosthenes
63
Bruns sieve
80
Selbergs sieve
113
The large sieve
135
The BombieriVinogradov theorem
156
The lower bound sieve
177
New directions in sieve theory
201
References
218
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About the author (2005)

Alina Carmen Cojocaru is an Instructor of Mathematics at Princeton University.

Ram Murty is a Professor and Queen's Reseach Chair at Queen's University.

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