My confusion comes from the fact that, although I know it's true what you said above (each \mathfrak{p}_n is its inverse in Cl_K, and also \mathfrak{p}_n \mathfrak{p}_m is principal), my problem is that
\mathfrak{p}_2 \mathfrak{p}_3 = 1
and
\mathfrak{p}_2 \mathfrak{p}_3 \mathfrak{p}_5 =...
As an exercise, I'm trying to compute the class number of K = \mathbb{Q}(\sqrt{30}). By the Minkowski bound, I just need to consider the prime ideals which divide 2,3,5.
I've found that
(2) = \mathfrak{p}^2_2
(3) = \mathfrak{p}^2_3
(5) = \mathfrak{p}^2_5
where...
I've started self-teaching asymptotic methods, and I have some theoretic questions (and lots of doubts!).
1. Say I have the asymptotic expansion
f(x) \asymp \alpha \sum_n a_n x^{-n}
for x large, where \alpha is some prefactor.
How can I estimate the value of n for the term of...