Given A and B integers relatively prime, we prove that almost all integers n in an interval of the form [N, N+H], where N exp(1/3+e) ≤ H ≤ N can be written as a sum Ap1 + Bp2 = n, with p1 and p2 primes and e an arbitrary positive constant. This generalizes the results of Perelli et al. (1985) established in the classical case A=B=1 (Goldbach's problem).
@article{urn:eudml:doc:44248,
title = {A short intervals result for linear equations in two prime variables.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {10},
year = {1997},
pages = {17-30},
zbl = {0882.11056},
mrnumber = {MR1452560},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44248}
}
Laporta, M. B. S. A short intervals result for linear equations in two prime variables.. Revista Matemática de la Universidad Complutense de Madrid, Tome 10 (1997) pp. 17-30. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44248/