A Higher-dimensional Sieve Method: With Procedures For Computing Sieve Functions (cambridge Tracts In Mathematics)
by Harold G. Diamond /
2008 / English / PDF
18.1 MB Download
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.
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.
