Let $p$ be an odd prime. This is a question about the class number of $Q(\sqrt p)$ and $Q(\sqrt-p)$,which we denote by $h(p)$ and $h(-p)$ respectively. While doing my research on number theory I came cross an obstacle to smooth which I have to know some relation between $h(p)$ and $h(-p)$. I only know some basic facts about algebraic number theory.
With some efforts, I only find the following paper, which provides some useful results when $p \equiv 3 \pmod 4$. Click here. That paper discussed the relation between $h(p)$ and $h(-p)$ in congruence sense (modular $p$), which is enough for me. However, I didn't find any similar result when $p \equiv 1 \pmod 4$.
I am desperate to know any facts about relation of $h(p)$ and $h(-p)$ when $p \equiv 1 \pmod 4$. Hope some experts could help me, thank you very much!!!
