LEADER 04018nam 2200697 a 450 001 9910452847303321 005 20200520144314.0 010 $a0-691-20299-0 010 $a1-283-84829-5 010 $a1-4008-4593-9 024 7 $a10.1515/9781400845934 035 $a(CKB)2550000000709081 035 $a(EBL)1062358 035 $a(OCoLC)823283433 035 $a(SSID)ssj0000785102 035 $a(PQKBManifestationID)11407248 035 $a(PQKBTitleCode)TC0000785102 035 $a(PQKBWorkID)10793628 035 $a(PQKB)11385431 035 $a(MiAaPQ)EBC1062358 035 $a(DE-B1597)447584 035 $a(OCoLC)979970266 035 $a(DE-B1597)9781400845934 035 $a(Au-PeEL)EBL1062358 035 $a(CaPaEBR)ebr10629460 035 $a(CaONFJC)MIL416079 035 $a(EXLCZ)992550000000709081 100 $a20070514d2007 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aPrime-detecting sieves$b[electronic resource] /$fGlyn Harman 205 $aCourse Book 210 $aPrinceton $cPrinceton University Press$dc2007 215 $a1 online resource (379 p.) 225 1 $aLondon Mathematical Society monographs series ;$vv. 33 300 $aDescription based upon print version of record. 311 $a0-691-12437-X 320 $aIncludes bibliographical references (p. [349]-359) and index. 327 $t Frontmatter -- $tContents -- $tPreface -- $tNotation -- $tChapter 1. Introduction -- $tChapter 2. The Vaughan Identity -- $tChapter 3. The Alternative Sieve -- $tChapter 4. The Rosser-Iwaniec Sieve -- $tChapter 5. Developing the Alternative Sieve -- $tChapter 6. An Upper-Bound Sieve -- $tChapter 7. Primes in Short Intervals -- $tChapter 8. The Brun-Titchmarsh Theorem on Average -- $tChapter 9. Primes in Almost All Intervals -- $tChapter 10. Combination with the Vector Sieve -- $tChapter 11. Generalizing to Algebraic Number Fields -- $tChapter 12. Variations on Gaussian Primes -- $tChapter 13. Primes of the Form x3 + 2y3 -- $tChapter 14. Epilogue -- $tAppendix -- $tBibliography -- $tIndex 330 $aThis book seeks to describe the rapid development in recent decades of sieve methods able to detect prime numbers. The subject began with Eratosthenes in antiquity, took on new shape with Legendre's form of the sieve, was substantially reworked by Ivan M. Vinogradov and Yuri V. Linnik, but came into its own with Robert C. Vaughan and important contributions from others, notably Roger Heath-Brown and Henryk Iwaniec. Prime-Detecting Sieves breaks new ground by bringing together several different types of problems that have been tackled with modern sieve methods and by discussing the ideas common to each, in particular the use of Type I and Type II information. No other book has undertaken such a systematic treatment of prime-detecting sieves. Among the many topics Glyn Harman covers are primes in short intervals, the greatest prime factor of the sequence of shifted primes, Goldbach numbers in short intervals, the distribution of Gaussian primes, and the recent work of John Friedlander and Iwaniec on primes that are a sum of a square and a fourth power, and Heath-Brown's work on primes represented as a cube plus twice a cube. This book contains much that is accessible to beginning graduate students, yet also provides insights that will benefit established researchers. 410 0$aLondon Mathematical Society monographs ;$vno. 33. 606 $aSieves (Mathematics) 606 $aNumbers, Prime 606 $aNumber theory 608 $aElectronic books. 615 0$aSieves (Mathematics) 615 0$aNumbers, Prime. 615 0$aNumber theory. 676 $a512.7/3 686 $aSK 180$2rvk 700 $aHarman$b G$g(Glyn),$f1956-$057162 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910452847303321 996 $aPrime detecting sieves$9711351 997 $aUNINA