Sieve Methods

Heine Halberstam, Hans Egon Richert, Hans Egon Richert

• Publisher: Dover Publications
• Year: 2013
• eBook ISBN: 9780486320809
• Topic: Mathematics
• Subtopic: Counting & Numeration
• Index: Mathematics

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.

Table of contents

• Cover
• Title Page
• Copyright Page
• Contents
• Preface to the Dover Edition
• Preface
• Notation
• Errata
• Introduction
• 1: The Sieve of Eratosthenes: Formulation of the C problem
• 2: The Combinatorial Sieve
• 3: The Simplest Selberg Upper Bound Method
• 4: The Selberg Upper Bound Method (continued): O-results
• 5: The Selberg Upper Bound Method: Explicit Estimates
• 6: An Extension of Selberg’s Upper Bound Method
• 7: Selberg’s Sieve Method (continued): A First Lower Bound
• 8: TheLinear Sieve
• 9: A Weighted Sieve: TheLinear Case
• 10: Weighted Sieves: The General Case
• 11: Chen’s Theorem
• Bibliography
• References