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

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Cambridge University Press, Oct 16, 2008 - Mathematics - 266 pages
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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.

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About the author (2008)

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.

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