000			02364nam a2200337Ia 4500
003			OSt
005			20250228230800.0
008			241112s9999 xx 000 0 und d
020			_a9780521888516 (hbk.) _c£ 111.00
040			_bENG _cIISER-BPR
041			_aENG
082			_a512.73 _bKOW _223rd
100			_aKowalski, E. _91082
222			_aMathematics
245		4	_aThe large sieve and applications : _bArithmetic geometry, random walks and discrete groups
250			_a1st ed.
260			_aCambridge: _bCambridge University Press, _cc2008.
300			_axxi, 293p. : _c24cm.
440			_aCambridge Tracts in Mathematics _vVol. 175 _93300
504			_aIncludes appendices, bibliographic references, and subject index.
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. * Explores new and surprising applications of the large sieve method, an important technique of analytic number theory * Presents applications in fields as wide ranging as topology, probability, arithmetic geometry and discrete group theory * Motivated, clear and self-contained discussions introduce readers to a technique previously confined to one field
650			_aMathematics _93301
650			_aAnalytic number theory _93302
650			_aSieve methods _93303
650			_aArithematic geometry _93304
650			_aDiscrete groups _93305
942			_cBK _2ddc
942			_2ddc
947			_a12110.099999999999
948			_a22
999			_c4222 _d4222