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.
- ISBN10 0511438656
- ISBN13 9780511438653
- Publish Date December 2008 (first published 1 January 2002)
- Publish Status Active
- Publish Country GB
- Publisher Cambridge University Press
- Imprint Cambridge University Press (Virtual Publishing)
- Format eBook
- Pages 290
- Language English