I was referring to the ones in Motl's blog. I wasn't aware this paper was updated compared to that one to remove those problems. Either way, looking at the paper I see a few things I can't follow. For example for theorem 1 he says for d>0 there exists \psi(y) = some expression uniformly for y≥1. The source he quotes is Montgomery's book on multiplicative number theory. Looking at the theorem in that book (Theorem 6.9) I can't see how what he says follows from it. The book is looking at the distribution of prime numbers with some error bounds. There is nothing in the paper about any sort of error bounds. Quite often such papers when submitted to arXiv get a quick look-over and if the professional mathematicians don't think it's worth much it gets thrown into the "General Mathematics" section, whereas more legitimate attempts would be put in the number theory section.