Abstract
We establish new mean value theorems for primes of size x x in arithmetic progressions to moduli as large as x 3 / 5 − ϵ x^{3/5-\epsilon } when summed with suitably well-factorable weights. This extends well-known work of Bombieri, Friedlander and Iwaniec, who handled moduli of size at most x 4 / 7 − ϵ x^{4/7-\epsilon } . This has consequences for the level of distribution for sieve weights coming from the linear sieve.
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