Often in math papers there is a series of constants appearing in estimates, each of which depends, sometimes in nonobvious ways, on those appearing earlier. Some authors like to give these constants genuine numerical values in order to help keep track of the dependencies between them and, in particular, to make sure that they aren't accidentally treating two different C's as the same. In delicate analytic proofs this sort of thing is particularly important - subtle missed dependencies are one of the places where serious proof attempts can go wrong in hard to find ways. I'm not saying this is what Zhang is doing, but it's one possibility.