Sifting Limits for the Λ^2Λ^- Sieve

Details Sifting Limits for the Λ^2Λ^- Sieve Sifting Limits for the Λ^2Λ^- Sieve

2010-12-17

arxiv.org/abs/1012.3809v1

Mathematics

Number Theory

Submitted to Journal of Number Theory

Scientific paper

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.

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