A Higher-Dimensional Sieve Method

Harold G. Diamond is Professor Emeritus in the Department of Mathematics at the University of Illinois at Urbana-Champaign. Heini Halberstam is Professor Emeritus in the Department of Mathematics at the University of Illinois at Urbana-Champaign. William F. Galway's research focuses on analytic and computational number theory. He is a member of the American Mathematical Society and of the Mathematical Association of America.

• List of tables; List of illustrations; Preface; 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 κ = 1: the linear sieve; 8. An application of the linear sieve; 9. A sieve method for κ > 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 condition; 14. Estimates of σκ (u) = jκ (u/2); 15. The pκ and qκ functions; 16. The zeros of Π−2 and Ξ; 17. The parameters σκ and βκ; 18. Properties of Fκ and fκ; Appendix 1. Methods for computing sieve functions; Bibliography; Index.

'… definitely of great interest to the intermediate-advanced sieve theorist.' Internationale Mathematische Nachrichten