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Higher dimensional sieve method : with procedures for computing sieve functions

By: Contributor(s): Material type: TextTextLanguage: English Series: Cambridge tracts in mathematics ; 177Publication details: Cambridge University Press Cambridge 2008Description: xxi, 266pISBN:
  • 9780521894876 (HB)
Subject(s):
Contents:
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
Summary: 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
Item type: BOOKS
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IMSc Library 511.337 DIA (Browse shelf(Opens below)) Available 61456

Includes index

Includes bibliography (p. 259-263)

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

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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The Institute of Mathematical Sciences, Chennai, India