Sifting Limits for the Λ^2Λ^- Sieve

Abstract

Sifting limits for the ${\Lambda }^2{\Lambda }^{-}$ sieve, Selberg's lower bound sieve, are computed for integral dimensions $1<\kappa \le 10$. The evidence strongly suggests that for all $\kappa \ge 3$ the ${\Lambda }^2{\Lambda }^{-}$ sieve is superior to the competing combinatorial sieves of Diamond, Halberstam, and Richert. A method initiated by Grupp and Richert for computing sieve functions for integral $\kappa$ is also outlined.

Submitted to Journal of Number Theory

Cited by in corpus (1)

• A family of multiple integrals connected with relatives of the Dickman function