Description 
1 online resource (xiv, 362 pages) : illustrations 
Series 
London Mathematical Society monographs series ; v. 33 

London Mathematical Society monographs ; new ser., no. 33.

Contents 
The Vaughan identity  The alternative sieve  The RosserIwaniec sieve  Developing the alternative sieve  An upperbound sieve  Primes in short intervals  The BrunTitchmarsh theorem on average  Primes in almost all intervals  Combination with the vector sieve  Generalizing to algebraic number fields  Variations on Gaussian primes  Primes of the form x [cubed] + 2y [cubed] 
Summary 
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 HeathBrown and Henryk Iwaniec. PrimeDetecting 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 primedetecting 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 HeathBrown'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 
Bibliography 
Includes bibliographical references (pages 349359) and index 
Notes 
English 

Print version record 
Subject 
Sieves (Mathematics)


Numbers, Prime.


Number theory.


MATHEMATICS  Number Theory.


Number theory


Numbers, Prime


Sieves (Mathematics)


Primzahl


Sieb


Zahlkörper

Form 
Electronic book

LC no. 
2007061051 
ISBN 
9781400845934 

1400845939 

1283848295 

9781283848299 
