The Large Sieve and its Applications: Arithmetic Geometry, Random Walks and Discrete Groups by E. Kowalski | 9780521888516 | Hardcover | Barnes & Noble
The Large Sieve and its Applications: Arithmetic Geometry, Random Walks and Discrete Groups

The Large Sieve and its Applications: Arithmetic Geometry, Random Walks and Discrete Groups

by E. Kowalski
     
 

ISBN-10: 0521888514

ISBN-13: 9780521888516

Pub. Date: 07/14/2008

Publisher: Cambridge University Press

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 realization that the underlying principles were capable of applications going well beyond prime number theory. This book

Overview

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 realization 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.

Product Details

ISBN-13:
9780521888516
Publisher:
Cambridge University Press
Publication date:
07/14/2008
Series:
Cambridge Tracts in Mathematics Series, #175
Pages:
316
Product dimensions:
6.10(w) x 9.00(h) x 1.00(d)

Table of Contents

Preface; Prerequisites and notation; 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; Appendix A. Small sieves; Appendix B. Local density computations over finite fields; Appendix C. Representation theory; Appendix D. Property (T) and Property (τ); Appendix E. Linear algebraic groups; Appendix F. Probability theory and random walks; Appendix G. Sums of multiplicative functions; Appendix H. Topology; Bibliography; Index.

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