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Sieve Methodsby Heini Halberstam
Synopses & Reviews
Derived from the techniques of analytic number theory, sieve theory employs methods from mathematical analysis to solve number-theoretical problems. This text by a noted pair of experts is regarded as the definitive work on the subject. It formulates the general sieve problem, explores the theoretical background, and illustrates significant applications.
"For years to come, Sieve Methods will be vital to those seeking to work in the subject, and also to those seeking to make applications," noted prominent mathematician Hugh Montgomery in his review of this volume for the Bulletin of the American Mathematical Society. The authors supply the theoretical background for the method of Jurkat-Richert and illustrate it by means of significant applications, concentrating on the "small" sieves of Brun and Selberg. Additional topics include the linear sieve, a weighted sieve, and Chen's theorem.
Originally published: London; New York: Academic Press, 1974.
This text by a noted pair of experts is regarded as the definitive work on sieve methods. It formulates the general sieve problem, explores the theoretical background, and illustrates significant applications. 1974 edition.
Table of Contents
Preface to the Dover Edition
1. Hypothesis H and Hn
2. Sieve Methods
3. Scope and Presentation
1. The Sieve of Eratosthenes: Formulation of the General Sieve Problem
2. The Combinatorial Sieve
3. The Simplest Seberg Upper Bound Method
4. The Selberg Upper Bound Method: Explicit Estimates
6. An Extension of Selberg's Upper Bound Method
7. Selberg's Sieve Method: A First Lower Bound
8. The Linear Sieve
9. A Weighted Sieve: The Linear Case
10. Weighted Sieves: The General Case
11. Chen's Theorem
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