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Prime-Detecting Sieves (LMS-33)

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Title: Prime-Detecting Sieves (LMS-33)
Description: 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.
Authors: Glyn Harman
Resource Type: eBook.
Subjects: Numbers, Prime, Sieves (Mathematics), Number theory
Categories: MATHEMATICS / Number Theory
Database: eBook Collection (EBSCOhost)
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  – Type: ebook-pdf
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Header DbId: nlebk
DbLabel: eBook Collection (EBSCOhost)
An: 507380
RelevancyScore: 1012
AccessLevel: 6
PubType: eBook
PubTypeId: ebook
PreciseRelevancyScore: 1011.53295898438
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  Data: Prime-Detecting Sieves (LMS-33)
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  Data: 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.
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RecordInfo BibRecord:
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    Classifications:
      – Code: 512.73
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Numbers, Prime
        Type: general
      – SubjectFull: Sieves (Mathematics)
        Type: general
      – SubjectFull: Number theory
        Type: general
    Titles:
      – TitleFull: Prime-Detecting Sieves (LMS-33)
        Type: main
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          Name:
            NameFull: Glyn Harman
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            NameFull: Glyn Harman
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          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2007
            – D: 04
              M: 02
              Type: profile
              Y: 2014
          Identifiers:
            – Type: isbn-print
              Value: 9780691124377
            – Type: isbn-print
              Value: 9780691202990
            – Type: isbn-electronic
              Value: 9781400845934
          Numbering:
            – Type: volume
              Value: 00033
          Titles:
            – TitleFull: Prime-Detecting Sieves (LMS-33)
              Type: main
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