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Prime-detecting sieves [electronic resource] / Glyn Harman.
Author
Harman, G. (Glyn), 1956-
[Browse]
Format
Book
Language
English
Εdition
Course Book
Published/Created
Princeton : Princeton University Press, c2007.
Description
1 online resource (379 p.)
Availability
Available Online
De Gruyter Princeton University Press eBook Package 2000-2013
De Gruyter Princeton University Press eBook-Package Backlist 2000-2013
Ebook Central Perpetual, DDA and Subscription Titles
Details
Subject(s)
Sieves (Mathematics)
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Numbers, Prime
[Browse]
Number theory
[Browse]
Series
London Mathematical Society monographs ; no. 33.
[More in this series]
London Mathematical Society monographs series ; v. 33
[More in this series]
Summary note
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.
Notes
Description based upon print version of record.
Bibliographic references
Includes bibliographical references (p. [349]-359) and index.
Language note
English
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
Show 18 more Contents items
Other format(s)
Issued also in print.
ISBN
0-691-20299-0
1-283-84829-5
1-4008-4593-9
OCLC
823283433
979970266
Doi
10.1515/9781400845934
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Princeton University Library aims to describe library materials in a manner that is respectful to the individuals and communities who create, use, and are represented in the collections we manage.
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Prime-detecting sieves / Glyn Harman.
id
9952614253506421
Prime-detecting sieves / Glyn Harman.
id
SCSB-9082751