Sifting Limits for the \Lambda^2\Lambda^- Sieve

Abstract

Sifting limits for the $\Lambda^{2}\Lambda^{-}$ sieve, Selberg's lower bound sieve, are computed for integral dimensions $1<\kappa\le10$. The evidence strongly suggests that for all $\kappa\ge3$ 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.