Thanks Franz. I find it interesting that he found in (3) of his theorem pretty much the same bound on the class group, since the one above is a bound on the narrow class group.

Thanks GH. I am hoping that this is new as an effective bound, and I have some ideas about how to improve it. BTW, I guess "$h(n^2+4)=1$ implies that $n$ is prime" must be qualified with $n \neq 4$?

Thanks. I checked that book out, and didn't find anything. Interestingly, Brezinski says "many results which were obtained during the nineteenth century are now completely forgotten and have to be rediscovered". Regardless, I'll go ahead and stick with the name "alternant".

Good question. I don't know.