Amazon.com: Prime-Detecting Sieves. (LMS-33) (London Mathematical Society Monographs): Books: Glyn Harman
This book seeks to describe the rapid development in recent decades of
sieve methods able to detect prime numbers. The subject began with
Eratosthenes in antiquity, took on new shape with Legendre's form of the
sieve, was substantially reworked by Ivan M. Vinogradov and Yuri V.
Linnik, but came into its own with Robert C. Vaughan and important
contributions from others, notably Roger Heath-Brown and Henryk Iwaniec.
Prime-Detecting Sieves breaks new ground by bringing together several
different types of problems that have been tackled with modern sieve
methods and by discussing the ideas common to each, in particular the
use of Type I and Type II information.
No other book has undertaken such a systematic treatment of
prime-detecting sieves. Among the many topics Glyn Harman covers are
primes in short intervals, the greatest prime factor of the sequence of
shifted primes, Goldbach numbers in short intervals, the distribution of
Gaussian primes, and the recent work of John Friedlander and Iwaniec on
primes that are a sum of a square and a fourth power, and Heath-Brown's
work on primes represented as a cube plus twice a cube. This book
contains much that is accessible to beginning graduate students, yet
also provides insights that will benefit established researchers.
About the Author
Glyn Harman is professor of pure mathematics at the University of
London, Royal Holloway. He is the author of "Metric Number Theory", the
coeditor of "Sieve Methods, Exponential Sums, and their Applications in
Number Theory", and the corecipient of the Hardy-Ramanujan award for his
work on primes in short intervals.