Series 
Cambridge tracts in mathematics ; 175 

Cambridge tracts in mathematics ;
175.

Subject 
Sieves (Mathematics)


Arithmetical algebraic geometry.


Random walks (Mathematics)


Discrete groups.

Description 
1 online resource (xxi, 293 pages) : illustrations. 
Bibliography Note 
Includes bibliographical references (pages 283288) and index. 
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. 
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 3manifolds; 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. 
Note 
Print version record. 
ISBN 
9780521888516 (hardback) 

0521888514 (hardback) 

9780511400919 (ebook) 

0511400918 (ebook) 

9780511397295 (electronic bk.) 

0511397291 (electronic bk.) 

0511398069 (electronic bk.) 

9780511398063 (electronic bk.) 
OCLC # 
316492258 
Additional Format 
Kowalski, Emmanuel, 1969 Large sieve and its applications. Cambridge, UK ; New York : Cambridge University Press, 2008 9780521888516 (DLC) 2008300417 (OCoLC)221147538 
