Sieve Methods - Brossura

Halberstam, Heini; Richert, Hans-Egon

Brossura

ISBN 10: 0486479390 ISBN 13: 9780486479392

Casa editrice: Dover Pubns, 2011

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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.

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Contenuti

Preface to the Dover Edition Preface Notation Introduction 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 Bibliography References