A higher-dimensional sieve method : with procedures for computing sieve functions /
As probability and combinatorics have penetrated the fabric of mathematical activity, sieve methods have become more versatile and sophisticated. This text explains the theory of higher dimensional sieves, examples of which are provided throughout.
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| Main Authors: | , , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge, U.K. ; New York :
Cambridge Univ. Press,
©2008.
|
| Series: | Cambridge tracts in mathematics ;
177. |
| Subjects: | |
| Online Access: | CONNECT |
Table of Contents:
- Cover; Title; Copyright; Dedication; Contents; List of Illustrations; List of Tables; Preface; Notation; Standard terminology; Sieve notation; Part I Sieves; 1 Introduction; 2 Selberg's sieve method; 3 Combinatorial foundations; 4 The Fundamental Lemma; 5 Selberg's sieve method (continued); 6 Combinatorial foundations (continued); 7 The case Kappa = 1: the linear sieve; 8 An application of the linear sieve; 9 A sieve method for Kappa> 1; 10 Some applications of Theorem 9.1; 11 A weighted sieve method; Part II Proof of the Main Analytic Theorem; 12 Dramatis personae and preliminaries
- 13 Strategy and a necessary condition14 Estimates of SigmaKappa(u) = jKappa(u/2); 15 The pKappa and qKappa functions; 16 The zeros of ... ; 17 The parameters AlphaKappa and BetaKappa; 18 Properties of FKappa and fKappa; Appendix 1 Procedures for computing sieve functions; A1.1 DDEs and the Iwaniec inner product; A1.2 The upper and lower bound sieve functions; A1.3 Using the Iwaniec inner product; A1.4 Some features of Mathematica; A1.5 Computing FKappa(u) and fKappa(u); A1.6 The function Ein(z); A1.7 Computing the adjoint functions; A1.8 Computing jKappa(u)
- A1.9 Computing AlphaKappa and BetaKappaA1.10 Weighted-sieve computations; Bibliography; Index
