The history and original paper of the Rosser–Iwaniec sieve I'm trying to find Rosser's original paper where he introduces his eponymous sieve. I've already found https://arxiv.org/pdf/math/0505521 (where the reference isn't given, but where it is indicated that Rosser has priority) and http://matwbn.icm.edu.pl/ksiazki/aa/aa36/aa36210.pdf (which is called "Rosser's sieve", but where there is no reference to his paper).
Any help would be very much appreciated.
 A: This is an addition to Lucia's remark. Check out in Selberg's collected papers entry #36: Sieve methods (Proc. Symp. Pure Math., 1971). There he writes:
Very important is also the unpublished work of Barkley Rosser who first settled the problem of the 1-residue sieve, and thus anticipated the work of Jurkat-Richert by about a decade. The part of §5 which deals with the Buchstab-Rosser sieve, refers to work done in the late 1950's after I had had the opportunity to see an unpublished manuscript by Rosser. [...] In the early 1950's Barkley Rosser devised a sieve procedure that essentially represents the limit of the Buchstab procedure. [...] Rosser's work was never published, but a paper about 10 years later by Jurkat and Richert [4] obtained essentially the same results for $k = 1$, by methods which combine Buchstab's ideas with estimations obtained by Brun's method and by a method mentioned in [6] and [7] for the upper bound. If one carefully analyzed
their method, it would probably turn out that this is really the Buchstab-Rosser sieve again.
