Sieve Methods

by Heine Halberstam, Hans Egon Richert

Derived from the techniques of analytic number theory, sieve theory employs methods from mathematical analysis to solve number-theoretical problems. This text by a noted pair of experts is regarded as the definitive work on the subject. It formulates the general sieve problem, explores the theoretical background, and illustrates significant applications. 1974 edition.

384 pages, Paperback

First published September 14, 2011

Reviews

[William Schram · Rating 3 out of 5]

Sieve Methods discusses the methods used to sieve out certain numbers, especially primes. I would say it requires a lot of background in number theory or some Analysis. In that vein, I would say I am not quite prepared to follow the contents of this book. As a Dover Publications reprint of an edition from 1974, it is quite good. It didn’t look like there were any typesetting errors or anything, though the first portion of the book counts up all the mistakes that were made in it and puts the corrections to those mistakes. There isn’t really much to say about this book. As far as Sieve Methods go, I was familiar with the Sieve of Erathosthenes where you take a number and try to divide it by the previous numbers to find if it is prime. I just hadn’t ever seen the proper mathematical expression for that. Apparently, they had come a long way since ancient times. As a side note, I especially liked how the book explained the symbols and notation used in the very first section.

To conclude, the book wasn’t bad, it just wasn’t very transparent about what it was.