A higher-dimensional sieve method
להגדלת הטקסט להקטנת הטקסט- ספר
Nearly a hundred years have passed since Viggo Brun invented his famous sieve, and the use of sieve methods is constantly evolving. As probability and combinatorics have penetrated the fabric of mathematical activity, sieve methods have become more versatile and sophisticated and in recent years have played a part in some of the most spectacular mathematical discoveries. Many arithmetical investigations encounter a combinatorial problem that requires a sieving argument, and this tract offers a modern and reliable guide in such situations. The theory of higher dimensional sieves is thoroughly explored, and examples are provided throughout. A Mathematica® software package for sieve-theoretical calculations is provided on the authors' website. To further benefit readers, the Appendix describes methods for computing sieve functions. These methods are generally applicable to the computation of other functions used in analytic number theory. The appendix also illustrates features of Mathematica® which aid in the computation of such functions.
כותר |
A higher-dimensional sieve method : with procedures for computing sieve functions / Harold G. Diamond, H. Halberstam, William F. Galway. [electronic resource] |
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מוציא לאור |
Cambridge : Cambridge University Press |
שנה |
2008 |
הערות |
Title from publisher's bibliographic system (viewed on 05 Oct 2015). Includes bibliographical references (p. 259-263) and index. English |
הערת תוכן ותקציר |
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 |
סדרה |
Cambridge tracts in mathematics 177 |
היקף החומר |
1 online resource (xxi, 266 pages) : digital, PDF file(s). |
שפה |
אנגלית |
מספר מערכת |
997010715427605171 |
תצוגת MARC
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