A Higher-Dimensional Sieve Method
With Procedures for Computing Sieve Functions
1st Edition
Published on 9. December 2008
978-0-511-43436-5 (ISBN)
Description
Nearly a hundred years have passed since Viggo Brun invented his famous sieve, and the use of sieve methods is constantly evolving. 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. 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 (R) software package for sieve-theoretical calculations is provided on the authors' website. To further benefit readers, the Appendix describes methods for computing sieve functions. These methods are generally applicable to the computation of other functions used in analytic number theory. The appendix also illustrates features of Mathematica (R) which aid in the computation of such functions.
Reviews / Votes
'... definitely of great interest to the intermediate-advanced sieve theorist.' Internationale Mathematische Nachrichten 'This is a well-crafted book, with clear writing.' MAA Reviews '... a very good source of details of techniques used in sieve methods and their applications, and therefore it can be warmly recommended for everyone interested in sieve methods.' EMS Newsletter 'Overall, this monograph is quite technical and is mostly aimed at people with a reasonable background in sieving theory. However, it is an excellent reference for anyone searching for the most up-to-date results in the theory.' Zentralblatt MATHMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Publishing group
Cambridge University Press
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises; 15 Tables, unspecified; 5 Halftones, unspecified
File size
18,68 MB
ISBN-13
978-0-511-43436-5 (9780511434365)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Harold G. Diamond | H. Halberstam | William F. Galway
A Higher-Dimensional Sieve Method
With Procedures for Computing Sieve Functions
Book
10/2008
Cambridge University Press
€153.80
Shipment within 15-20 days
Persons
Harold G. Diamond is Professor Emeritus in the Department of Mathematics at the University of Illinois at Urbana-Champaign. Heini Halberstam is Professor Emeritus in the Department of Mathematics at the University of Illinois at Urbana-Champaign. William F. Galway's research focuses on analytic and computational number theory. He is a member of the American Mathematical Society and of the Mathematical Association of America.
Content
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 ? = 1: the linear sieve; 8. An application of the linear sieve; 9. A sieve method for ? > 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 ?? (u) = j? (u/2); 15. The p? and q? functions; 16. The zeros of ??2 and ?; 17. The parameters ?? and ??; 18. Properties of F? and f?; Appendix 1. Methods for computing sieve functions; Bibliography; Index.
