The Large Sieve and its Applications Arithmetic Geometry Random Walks and Discrete Groups 1st Edition by E Kowalski ISBN 0521888514 9780521888516

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Product details:

ISBN 10: 0521888514

ISBN 13: 9780521888516 

Author: E. Kowalski 

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.

Table of contents:

Preface
Acknowledgments
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
References
Index

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Tags: E Kowalski, Large Sieve, Applications, Arithmetic, Geometry, Random Walks, Discrete Groups