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Prime-Detectin
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- Sofort-KaufenPrime-Detecting Sieves -- (London Mathematical Society Monographs) - Hardcover
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eBay-Artikelnr.:376448959622
Artikelmerkmale
- Artikelzustand
- Release Year
- 2007
- Book Title
- Prime-Detecting Sieves (LMS-33) (London Mathematical Society M...
- ISBN
- 9780691124377
Über dieses Produkt
Product Identifiers
Publisher
Princeton University Press
ISBN-10
069112437X
ISBN-13
9780691124377
eBay Product ID (ePID)
10038425433
Product Key Features
Number of Pages
384 Pages
Publication Name
Prime-Detecting Sieves (Lms-33)
Language
English
Subject
Ancient / Rome, Number Theory
Publication Year
2007
Type
Textbook
Subject Area
Mathematics, History
Series
London Mathematical Society Monographs
Format
Hardcover
Dimensions
Item Height
1.1 in
Item Weight
21 Oz
Item Length
9.5 in
Item Width
6.5 in
Additional Product Features
Intended Audience
College Audience
LCCN
2007-061051
Dewey Edition
22
Reviews
This book provides a very nice introduction to a very active and important area of research. Several chapters include discussion of the limitations of the given methods; this is an unusual feature but a very useful one to readers. There is also helpful discussion of historical developments of the given methods. This a valuable book, both for researchers and for advanced graduate students in analytic number theory. ---S. W Graham, Mathematical Reviews, The book is written in a very accessible style for a wide spectrum of readers. . . . Besides mathematical ideas, the presentation also contains many important historical comments, which make the book useful for a general mathematical audience trying to orient themselves in the evolution of the main techniques applied in sieve methods., "The book is written in a very accessible style for a wide spectrum of readers. . . . Besides mathematical ideas, the presentation also contains many important historical comments, which make the book useful for a general mathematical audience trying to orient themselves in the evolution of the main techniques applied in sieve methods." -- EMS Newsletter, "[T]his book contains a valuable compendium of methods and results, and it will be of interest to aficionados of prime number theory."-- Harold G. Diamond, SIAM Review, "The book is written in a very accessible style for a wide spectrum of readers. . . . Besides mathematical ideas, the presentation also contains many important historical comments, which make the book useful for a general mathematical audience trying to orient themselves in the evolution of the main techniques applied in sieve methods."-- EMS Newsletter, The book is written in a very accessible style for a wide spectrum of readers. . . . Besides mathematical ideas, the presentation also contains many important historical comments, which make the book useful for a general mathematical audience trying to orient themselves in the evolution of the main techniques applied in sieve methods. -- EMS Newsletter, "[T]his book contains a valuable compendium of methods and results, and it will be of interest to aficionados of prime number theory." --Harold G. Diamond, SIAM Review, [T]his book contains a valuable compendium of methods and results, and it will be of interest to aficionados of prime number theory. -- Harold G. Diamond, SIAM Review, "This book provides a very nice introduction to a very active and important area of research. Several chapters include discussion of the limitations of the given methods; this is an unusual feature but a very useful one to readers. There is also helpful discussion of historical developments of the given methods. This a valuable book, both for researchers and for advanced graduate students in analytic number theory." --S. W Graham, Mathematical Reviews, This book provides a very nice introduction to a very active and important area of research. Several chapters include discussion of the limitations of the given methods; this is an unusual feature but a very useful one to readers. There is also helpful discussion of historical developments of the given methods. This a valuable book, both for researchers and for advanced graduate students in analytic number theory., "This book provides a very nice introduction to a very active and important area of research. Several chapters include discussion of the limitations of the given methods; this is an unusual feature but a very useful one to readers. There is also helpful discussion of historical developments of the given methods. This a valuable book, both for researchers and for advanced graduate students in analytic number theory."-- S. W Graham, Mathematical Reviews, This book provides a very nice introduction to a very active and important area of research. Several chapters include discussion of the limitations of the given methods; this is an unusual feature but a very useful one to readers. There is also helpful discussion of historical developments of the given methods. This a valuable book, both for researchers and for advanced graduate students in analytic number theory. -- S. W Graham, Mathematical Reviews, [T]his book contains a valuable compendium of methods and results, and it will be of interest to aficionados of prime number theory. ---Harold G. Diamond, SIAM Review, [T]his book contains a valuable compendium of methods and results, and it will be of interest to aficionados of prime number theory.
Series Volume Number
1
Illustrated
Yes
Dewey Decimal
512.73
Table Of Content
Preface xi Notation xiii Chapter 1. Introduction 1 Chapter 2. The Vaughan Identity 25 Chapter 3. The Alternative Sieve 47 Chapter 4. The Rosser-Iwaniec Sieve 65 Chapter 5. Developing the Alternative Sieve 83 Chapter 6. An Upper-Bound Sieve 103 Chapter 7. Primes in Short Intervals 119 Chapter 8. The Brun-Titchmarsh Theorem on Average 157 Chapter 9. Primes in Almost All Intervals 189 Chapter 10. Combination with the Vector Sieve 201 Chapter 11. Generalizing to Algebraic Number Fields 231 Chapter 12. Variations on Gaussian Primes 265 Chapter 13. Primes of the Form x 3 + 2y 3 303 Chapter 14. Epilogue 335 Appendix 337 Bibliography 349 Index 361
Synopsis
Seeks to describe the development in recent decades of sieve methods able to detect prime numbers. This work covers topics such as; 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., 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., 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.
LC Classification Number
QA246.H375 2007
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