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arXiv · 1205.0413

When the sieve works

Andrew Granville·Dimitris Koukoulopoulos·Kaisa Matomäki
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Abstract

We are interested in classifying those sets of primes $\mathcal{P}$ such that when we sieve out the integers up to $x$ by the primes in $\mathcal{P}^c$ we are left with roughly the expected number of unsieved integers. In particular, we obtain the first general results for sieving an interval of length $x$ with primes including some in $(\sqrt{x},x]$, using methods motivated by additive combinatorics.

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Andrew Granville, Dimitris Koukoulopoulos, Kaisa Matomäki. 2012-05-02. When the sieve works. https://doi.org/10.1215/00127094-3120891

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