Prime-detecting sieves / Glyn Harman.

Format:

Book

Author/Creator:

Harman, G. (Glyn), 1956-

Series:

London Mathematical Society monographs ; no. 33.

London Mathematical Society monographs series ; v. 33

Language:

English

Subjects (All):

Sieves (Mathematics).

Numbers, Prime.

Number theory.

Physical Description:

1 online resource (379 p.)

Edition:

Course Book

Place of Publication:

Princeton : Princeton University Press, c2007.

Language Note:

English

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 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.

Contents:

Frontmatter

Contents

Preface

Notation

Chapter 1. Introduction

Chapter 2. The Vaughan Identity

Chapter 3. The Alternative Sieve

Chapter 4. The Rosser-Iwaniec Sieve

Chapter 5. Developing the Alternative Sieve

Chapter 6. An Upper-Bound Sieve

Chapter 7. Primes in Short Intervals

Chapter 8. The Brun-Titchmarsh Theorem on Average

Chapter 9. Primes in Almost All Intervals

Chapter 10. Combination with the Vector Sieve

Chapter 11. Generalizing to Algebraic Number Fields

Chapter 12. Variations on Gaussian Primes

Chapter 13. Primes of the Form x3 + 2y3

Chapter 14. Epilogue

Appendix

Bibliography

Index

Notes:

Description based upon print version of record.

Includes bibliographical references (p. [349]-359) and index.

ISBN:

9780691202990

0691202990

9781283848299

1283848295

9781400845934

1400845939

OCLC:

823283433