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We establish new mean value theorems for primes of size $x$ in arithmetic progressions to moduli as large as $x^{3/5-\epsilon}$ when summed with suitably well-factorable weights.
On the large sieve
E. Bombieri · 1965
Earlier work this paper cites.
The density hypothesis for Dirichet L L -series
A. I. Vinogradov · 1965
Earlier work this paper cites.
A conjecture in prime number theory
P. D. T. A. Elliott and H. Halberstam · 1970
Earlier work this paper cites.
On the representation of a larger even integer as the sum of a prime and the product of at most two primes
J.-R. Chen · 1973
Earlier work this paper cites.
A new form of the error term in the linear sieve
H. Iwaniec · 1980
Earlier work this paper cites.
A Brun-Titchmarsh theorem for multiplicative functions
P. Shiu · 1980
Earlier work this paper cites.
Kloosterman sums and Fourier coefficients of cusp forms
J.-M. Deshouillers and H. Iwaniec · 1982
Cited alongside, same era.
Prime numbers in short intervals and a generalized Vaughan identity
D. R. Heath-Brown · 1982
Cited alongside, same era.
Primes in arithmetic progressions to large moduli
E. Bombieri, J. Friedlander, and H. Iwaniec · 1986
Cited alongside, same era.
On the switching principle in sieve theory
É. Fouvry and F. Grupp · 1986
Cited alongside, same era.
Primes in arithmetic progressions to large moduli. II
E. Bombieri, J. Friedlander, and H. Iwaniec · 1987
Cited alongside, same era.
Weighted sieves and twin prime type equations
É. Fouvry and F. Grupp · 1989
Cited alongside, same era.
The divisor function over arithmetic progressions
Étienne Fouvry and Henryk Iwaniec · 1992
Later among the works it cites.
Chen’s double sieve, Goldbach’s conjecture and the twin prime problem
J. Wu · 2004
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Primes in arithmetic progressions to large moduli I: Fixed residue classes
J. Maynard · 2006
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Prime-detecting sieves
G. Harman · 2007
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Opera de cribro
J. Friedlander and H. Iwaniec · 2010
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Théorèmes de type Fouvry-Iwaniec pour les entiers friables
S. Drappeau · 2015
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