The large sieve and its applications : arithmetic geometry, random walks and discrete groups / E. Kowalski.

Format:

Book

Author/Creator:

Kowalski, Emmanuel, 1969- author.

Series:

Cambridge tracts in mathematics ; 175.

Cambridge tracts in mathematics ; 175

Language:

English

Subjects (All):

Sieves (Mathematics).

Arithmetical algebraic geometry.

Random walks (Mathematics).

Discrete groups.

Physical Description:

1 online resource (xxi, 293 pages) : digital, PDF file(s).

Edition:

1st ed.

Other Title:

The Large Sieve & its Applications

Place of Publication:

Cambridge : Cambridge University Press, 2008.

Language Note:

English

Summary:

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.

Contents:

1. Introduction

2. The principle of the large sieve

3. Group and conjugacy sieves

4. Elementary and classical examples

5. Degrees of representations of finite groups

6. Probabilistic sieves

7. Sieving in discrete groups

8. Sieving for Frobenius over finite fields

App. A. Small sieves

App. B. Local density computations over finite fields

App. C. Representation theory

App. D. Property (T) and Property ([tau])

App. E. Linear algebraic groups

App. F. Probability theory and random walks

App. G. Sums of multiplicative functions

App. H. Topology.

Notes:

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

Includes bibliographical references and index.

ISBN:

1-107-18739-7

1-281-38384-8

9786611383848

0-511-39806-9

0-511-39729-1

0-511-40091-8

0-511-39656-2

0-511-54294-1

0-511-39887-5

OCLC:

437209200