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We prove that the primes below $x$ are, on average, equidistributed in arithmetic progressions to smooth moduli of size up to $x^{1/2+1/40-\epsilon}$.
On the large sieve
Bombieri, E · 1965
Earlier work this paper cites.
The density hypothesis for Dirichet L-series
Vinogradov, A. I · 1965
Earlier work this paper cites.
Primes in arithmetic progressions
Fouvry, E., and Iwaniec, H · 1983
Earlier work this paper cites.
Primes in arithmetic progressions to large moduli
Bombieri, E., Friedlander, J., and Iwaniec, H · 1986
Earlier work this paper cites.
Integers without large prime factors
Hildebrand, A., and Tenenbaum, G · 1993
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A ternary diophantine inequality over primes
Baker, R., and Weingartner, A · 2014
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Variants of the Selberg sieve, and bounded intervals containing many primes
Polymath, D. H. J · 2014
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Bounded gaps between primes
Zhang, Y · 2014
Cited alongside, same era.
Primes in arithmetic progressions to large moduli, and Goldbach beyond the square-root barrier
Lichtman, J. D
Cited in the paper.
Primes in arithmetic progressions to large moduli I: Fixed residue classes
Maynard, J
Cited in the paper.
Primes in arithmetic progressions to large moduli II: Well-factorable estimates
Maynard, J
Cited in the paper.
Primes in arithmetic progressions to large moduli III: Uniform residue classes
Maynard, J
Cited in the paper.
Large sieve inequalities for exceptional Maass forms and applications
Pascadi, A
Cited in the paper.
Small gaps between primes
Maynard, J · 2015
Later among the works it cites.
Bounded intervals containing many primes
Baker, R. C., and Irving, A. J · 2017
Later among the works it cites.
New equidistribution estimates of Zhang type
Polymath, D. H. J · 2067
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