000			03000nam a22003978i 4500
001			CR9780511542947
003			UkCbUP
005			20200124160233.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			090505s2008||||enk o ||1 0|eng|d
020			_a9780511542947 (ebook)
020			_z9780521888516 (hardback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA242.5 _b.K69 2008
082	0	4	_a512.73 _222
100	1		_aKowalski, Emmanuel, _d1969- _eauthor.
245	1	4	_aThe large sieve and its applications : _barithmetic geometry, random walks and discrete groups / _cE. Kowalski.
246	3		_aThe Large Sieve & its Applications
264		1	_aCambridge : _bCambridge University Press, _c2008.
300			_a1 online resource (xxi, 293 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aCambridge tracts in mathematics ; _v175
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0	0	_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.
520			_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.
650		0	_aSieves (Mathematics)
650		0	_aArithmetical algebraic geometry.
650		0	_aRandom walks (Mathematics)
650		0	_aDiscrete groups.
776	0	8	_iPrint version: _z9780521888516
830		0	_aCambridge tracts in mathematics ; _v175.
856	4	0	_uhttps://doi.org/10.1017/CBO9780511542947
999			_c517791 _d517789