A Higher-Dimensional Sieve Method
With Procedures for Computing Sieve Functions
$142.00 (C)
Part of Cambridge Tracts in Mathematics
- Authors:
- Harold G. Diamond, University of Illinois, Urbana-Champaign
- H. Halberstam, University of Illinois, Urbana-Champaign
- William F. Galway
- Date Published: November 2008
- availability: Available
- format: Hardback
- isbn: 9780521894876
$
142.00
(C)
Hardback
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As probability and combinatorics have penetrated the fabric of mathematical activity, sieve methods have become more versatile and sophisticated and in recent years have played a part in some of the most spectacular mathematical discoveries. Nearly a hundred years have passed since Viggo Brun invented his famous sieve, and the use of sieve methods is constantly evolving. Many arithmetical investigations encounter a combinatorial problem that requires a sieving argument, and this tract offers a modern and reliable guide in such situations. The theory of higher dimensional sieves is thoroughly explored, and examples are provided throughout. A Mathematica® software package for sieve-theoretical calculations is provided on the authors' website. To further benefit readers, the Appendix describes methods for computing sieve functions.
Read more- Fully explains the theory of higher dimensional sieves using many examples
- Modern and reliable guide for researchers needing to solve combinatorial problems with sieving arguments
- Computational methods are explained in detail in an appendix and on the accompanying website
Reviews & endorsements
"This is a well crafted book, with clear writing."
Allen Stenger, MAA ReviewsSee more reviews"It is to be recommended on the one hand for the serious student of the subject, and on the other for those who want a reference to the strongest available results for applications."
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×Product details
- Date Published: November 2008
- format: Hardback
- isbn: 9780521894876
- length: 290 pages
- dimensions: 235 x 155 x 20 mm
- weight: 0.52kg
- contains: 5 b/w illus. 15 tables
- availability: Available
Table of Contents
List of tables
List of illustrations
Preface
Notation
Part I. Sieves:
1. Introduction
2. Selberg's sieve method
3. Combinatorial foundations
4. The fundamental Lemma
5. Selberg's sieve method (continued)
6. Combinatorial foundations (continued)
7. The case κ = 1: the linear sieve
8. An application of the linear sieve
9. A sieve method for κ > 1
10. Some applications of Theorem 9.1
11. A weighted sieve method
Part II. Proof of the Main Analytic Theorem:
12. Dramatis personae and preliminaries
13. Strategy and a necessary condition
14. Estimates of σκ (u) = jκ (u/2)
15. The pκ and qκ functions
16. The zeros of Π−2 and Ξ
17. The parameters σκ and βκ
18. Properties of Fκ and fκ
Appendix 1. Methods for computing sieve functions
Bibliography
Index.-
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