Duke Mathematical Journal

When the sieve works

Andrew Granville, Dimitris Koukoulopoulos, and Kaisa Matomäki

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We are interested in classifying those sets of primes P such that when we sieve out the integers up to x by the primes in 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 ( x , x ] , using methods motivated by additive combinatorics.

Article information

Duke Math. J. Volume 164, Number 10 (2015), 1935-1969.

Received: 20 December 2013
Revised: 9 September 2014
First available in Project Euclid: 14 July 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11N35: Sieves
Secondary: 11B30: Arithmetic combinatorics; higher degree uniformity

sieve methods additive combinatorics continuous postage stamp problem Balog–Szemeredi–Gowers theorem Ruzsa–Chang theorem


Granville, Andrew; Koukoulopoulos, Dimitris; Matomäki, Kaisa. When the sieve works. Duke Math. J. 164 (2015), no. 10, 1935--1969. doi:10.1215/00127094-3120891. https://projecteuclid.org/euclid.dmj/1436909415

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