Craig Franze

Sifting Limits for the Λ^2Λ^- Sieve

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