Question

Hi,

Could anyone tell me in what sense the following is an "asymptotic formula":

Theorem 1 from

http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.mmj/1029000373

(this is open access, so I think I'm allowed to link it)

At the moment, I'm just trying to understand what the bit with Q $Q\leq x$ means. I assume the Theorem says something like: the LHS varies like the main term, in that LHS/[main term] tends to one as x tends to infinity. But it's not clear to me that [error terms]/[main terms] tend to zero. There seems to be definitely something I'm not understanding with the relationship between $Q$ and $x$.

Can anyone clarify?

Thanks very much.