Sieving both sides vs one side at a time
My line siever currently sieves N(a+bθ)*(a+bm), which is the algebraic side and the rational side at the same time. However, it looks like most papers point to sieving the two sides separately. What is the advantage of this? Won't this need extra work, like matching (a,b)pair of both sides, since both sides need to be smooth?
