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The large sieve and its applications...

Kowalski, Emmanuel, (1969-)

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The large sieve and its applications = arithmetic geometry, random walks and discrete groups /

Record Type:	Electronic resources : Monograph/item
Title/Author:	The large sieve and its applications/ E. Kowalski.
Reminder of title:	arithmetic geometry, random walks and discrete groups /
remainder title:	The Large Sieve & its Applications
Author:	Kowalski, Emmanuel,
Published:	Cambridge :Cambridge University Press, : 2008.,
Description:	xxi, 293 p. :ill., digital ;24 cm.
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Subject:	Sieves (Mathematics) -
Online resource:	https://doi.org/10.1017/CBO9780511542947
ISBN:	9780511542947

The large sieve and its applications = arithmetic geometry, random walks and discrete groups /
Kowalski, Emmanuel,1969-

The large sieve and its applicationsarithmetic geometry, random walks and discrete groups /[electronic resource] :The Large Sieve & its ApplicationsE. Kowalski. - Cambridge :Cambridge University Press,2008. - xxi, 293 p. :ill., digital ;24 cm. - Cambridge tracts in mathematics ;175. - Cambridge tracts in mathematics ;175..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Introduction --1.

Among 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.

ISBN: 9780511542947Subjects--Topical Terms:

705221
Sieves (Mathematics)

LC Class. No.: QA242.5 / .K69 2008

Dewey Class. No.: 512.73

The large sieve and its applications = arithmetic geometry, random walks and discrete groups /
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245 1 4 $a The large sieve and its applications $h [electronic resource] : $b arithmetic geometry, random walks and discrete groups / $c E. Kowalski.
246 3 $a The Large Sieve & its Applications
260 $a Cambridge : $b Cambridge University Press, $c 2008.
300 $a xxi, 293 p. : $b ill., digital ; $c 24 cm.
490 1 $a Cambridge tracts in mathematics ; $v 175
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 0 $g 1. $t Introduction -- $g 2. $t The principle of the large sieve -- $g 3. $t Group and conjugacy sieves -- $g 4. $t Elementary and classical examples -- $g 5. $t Degrees of representations of finite groups -- $g 6. $t Probabilistic sieves -- $g 7. $t Sieving in discrete groups -- $g 8. $t Sieving for Frobenius over finite fields -- $g App. A. $t Small sieves -- $g App. B. $t Local density computations over finite fields -- $g App. C. $t Representation theory -- $g App. D. $t Property (T) and Property ([tau]) -- $g App. E. $t Linear algebraic groups -- $g App. F. $t Probability theory and random walks -- $g App. G. $t Sums of multiplicative functions -- $g App. H. $t Topology.
520 $a Among 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 $a Sieves (Mathematics) $3 705221
650 0 $a Arithmetical algebraic geometry. $3 699672
650 0 $a Random walks (Mathematics) $3 532102
650 0 $a Discrete groups. $3 661794
830 0 $a Cambridge tracts in mathematics ; $v 175. $3 3470490
856 4 0 $u https://doi.org/10.1017/CBO9780511542947