A Higher-Dimensional Sieve Method: With Procedures for Computing Sieve Functions
Harold G. Diamond, H. Halberstam, William F. Galway - A Higher-Dimensional Sieve Method: With Procedures for Computing Sieve Functions
Published: 2008-11-03 | ISBN: 0521894875 | PDF | 290 pages | 18 MB
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.