Higher-Dimensional Sieve Method: With Procedures for Computing Sieve Functions

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.

Modern and practical guide to higher dimensional sieve theory, with an Appendix describing methods for computing sieve functions.

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.