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101 0 $aeng
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181   $ctxt$2rdacontent
182   $cc$2rdamedia
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200 14$aThe large sieve and its applications $earithmetic geometry, random walks and discrete groups /$fE. Kowalski$b[electronic resource]
210  1$aCambridge :$cCambridge University Press,$d2008.
215   $a1 online resource (xxi, 293 pages) $cdigital, PDF file(s)
225 1 $aCambridge tracts in mathematics ;$v175
300   $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
311   $a0-521-88851-4 
320   $aIncludes bibliographical references and index.
327   $g1.$tIntroduction --$g2.$tThe principle of the large sieve --$g3.$tGroup and conjugacy sieves --$g4.$tElementary and classical examples --$g5.$tDegrees of representations of finite groups --$g6.$tProbabilistic sieves --$g7.$tSieving in discrete groups --$g8.$tSieving for Frobenius over finite fields --$gApp. A.$tSmall sieves --$gApp. B.$tLocal density computations over finite fields --$gApp. C.$tRepresentation theory --$gApp. D.$tProperty (T) and Property ([tau]) --$gApp. E.$tLinear algebraic groups --$gApp. F.$tProbability theory and random walks --$gApp. G.$tSums of multiplicative functions --$gApp. H.$tTopology.
330   $aAmong the modern methods used to study prime numbers, the 'sieve' has been one of the most efficient. Originally conceived by Linnik in 1941, the 'large sieve' has developed extensively since the 1960s, with a recent realisation that the underlying principles were capable of applications going well beyond prime number theory. This book develops a general form of sieve inequality, and describes its varied applications, including the study of families of zeta functions of algebraic curves over finite fields; arithmetic properties of characteristic polynomials of random unimodular matrices; homological properties of random 3-manifolds; and the average number of primes dividing the denominators of rational points on elliptic curves. Also covered in detail are the tools of harmonic analysis used to implement the forms of the large sieve inequality, including the Riemann Hypothesis over finite fields, and Property (T) or Property (tau) for discrete groups.
410  0$aCambridge tracts in mathematics ;$v175.
517 3 $aThe Large Sieve & its Applications
606   $aSieves (Mathematics)
606   $aArithmetical algebraic geometry
606   $aRandom walks (Mathematics)
606   $aDiscrete groups
615  0$aSieves (Mathematics)
615  0$aArithmetical algebraic geometry.
615  0$aRandom walks (Mathematics)
615  0$aDiscrete groups.
676   $a512.73
700   $aKowalski$b Emmanuel$f1969-$0853654
801  0$bUkCbUP
801  1$bUkCbUP
906   $aBOOK
912   $a9910451434203321
996   $aThe large sieve and its applications$91906049
997   $aUNINA